Boundary Value Problem - Science topic

In this paper, we introduce new second order dynamical system approach for solving a class of mixed general variational inequalities. Using the forward finite difference schemes, we suggest some multi-step iterative methods for solving the mixed variational inequalities. Convergence analysis is investigated under certain mild conditions. Some speci...

The main goal of this work is to study the effect of applying Lagrange's polynomials on finding the numerical solutions of many different neutrosophic boundary value problems, where we use those polynomials to solve three different neutrosophic boundary value problems numerically, and we present many numerical tables to compare the accuracy of the...

We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$ with $p \in (1,\infty$). We also propose and analyze a convergent finite element discretization for the nonli...

Preflip and elliptic boundary value problem.

The present research explores the existence of positive solutions for the iterative system of higher-order differential equations with integral boundary conditions that include a non-homogeneous term. To address the boundary value problem, the solution is expressed as a solution of an equivalent integral equation involving kernels. Subsequently, bo...

In order to study spatial distributions of global magnetosheath structures, physicists often rely upon spatial binning, whereby space is divided into cells, each filled with the average value of all spacecraft measurements within that cell. The traditional binning schema utilizes a fixed Cartesian grid of cube bins. The morphology of the magnetoshe...

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the resulting coupled evolutionary system, the macroscopic fluid velocity field $\boldsymbol{v}$ satisfies a Navier--St...

This paper discusses a class of Kirchhoff boundary value problem that involve the fractional τ(·)-Laplacian operator of the form α + β[u] s,τ (−∆) s τ(x,·) u(x) + |u(x)| r(x)−2 u(x) = ξ|u(x)| µ(x)−2 u(x) in Ω, u = 0 in R N \Ω. where Ω is a smooth bounded domain in R N , (N ≥ 2), 0 < s < 1, ξ is a positive parameter. Utilizing Berkovits degree theor...

The numerical solution to boundary differential problems is a crucial task in modern applied mathematics. Usually, implicit integration methods are applied to solve this class of problems due to their high numerical stability and convergence. The known shortcoming of implicit algorithms is high computational costs, which can become unacceptable in...

This is a one-semester course on Nonlinear Boundary Value Problems in German language. It is for free use. Comments and corrections are welcome - send them to Rainer.Mandel@gmx.de.

In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uni...

This work investigates the solution of fractional orders for α∈(1,2] and t∈(0,a] considering boundary value problem with two boundary value conditions known as T Regge problem for fractional order. Additionally, a set of fractional boundary value problem equations is analyzed. The solution was provided. The key results are shown using the Kharrat-T...

We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that mi...

In this paper, we study a certain type of noisy tug-of-war game which can be regarded as an interpretation of a certain type of boundary value problem for the normalized $p$-Laplace equation, where $1<p<\infty$. More precisely, we will investigate the boundary regularity of the value function to the game and its convergence to a viscosity solution...

In this paper, we establish sufficient conditions to guarantee some existence results of nontrivial solutions for a class of nonlinear boundary value problem posed on an unbounded interval of $\mathbb R$. According to the behavior of the nonlinear term, an effective operator is considered. Our main tool is especially Schauder's fixed point theorem...

Landfilling of municipal solid waste generates a number of problems. This article focuses on one of them – the settling of the landfill surface due to organic residue biodegradation. The task of predicting the settlement of the waste storage surface is roposed to be solved within the framework of the theory of filtration consolidation of porous med...

We study a Dirichlet optimal control problem for a quasilinear monotone el-liptic equation with the so-called weighted p(x)-Laplace operator. The coefficient of the p(x)-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L ∞ (Ω). In this article, we use box-type constraints for the admissible controls. In order to handle the inherent degener...

In this paper, we construct the fundamental solution of one boundary value problem on the geometric middle of the domain for an integro-differential equation of 3D Bianchi type with a dominant mixed derivative of third order with nonsmooth coefficients. Key Words and Phrases: integro-differential equations, boundary value problem on the geometric m...

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel’skiĭ cone compression–expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex se...

In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter λ. Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for thi...

We investigate the existence of multiple positive solutions for the following Dirichlet boundary value problem: \begin{equation*} \begin{aligned} -\Delta_p u + (-\Delta_p)^s u = \lambda \frac{f(u)}{u^{\beta}}\ \text{in} \ \Omega\newline u >0\ \text{in} \ \Omega,\ u =0\ \text{in} \ \mathbb{R}^N \setminus \Omega \end{aligned} \end{equation*} where $\...

In this paper, we explore multi positive solutions together with their existence and uniqueness, which is properly defined for delta fractional version of Riemann-Liouville difference operators. Our exploration encompasses two distinct directions. In the first direction, we construct the Green's function formula for the proposed delta fractional bo...

Traction force microscopy is a method widely used in biophysics and cell biology to determine forces that biological cells apply to their environment. In the experiment, the cells adhere to a soft elastic substrate, which is then deformed in response to cellular traction forces. The inverse problem consists in computing the traction stress applied...

This paper analytically investigates the vertical dynamic response of a rigid strip foundation on layered unsaturated media. Using the triphasic Biot-type model and extended precise integration method, we derive the flexibility coefficient for layered unsaturated media. On this basis, by introducing the Bessel function series of the first kind, the...

We prove existence and uniqueness theorems for regular solutions to boundary value problems for ultraparabolic differential equations with temporal variables \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\od...

In this paper, we investigate the global properties of Fourier multipliers in the setting of nonharmonic analysis of boundary value problems. We give necessary and sufficient conditions for a Fourier multiplier to be globally hypoelliptic and also to be globally solvable. As an application, we consider operators on \documentclass[12pt]{minimal} \us...

In this paper, we introduce a new class of contractions in normed spaces, referred to as generalized enriched Kannan contractions. These contractions expand the familiar enriched Kannan contractions to three-point versions, broadening the scope of Kannan contractions. These mappings are typically discontinuous, except at the fixed points, where the...

First of all, we study the Hilbert boundary value problem for the Beltrami equations with sources in Jordan domains of the complex plane. Assuming that the coefficient of the problem is a function of countable bounded variation and the boundary date is measurable with respect to the logarithmic capacity, we prove the existence of nonclassical solut...

Fractional differential equations (FDEs) have gained significant attention due to their ability to model complex physical phenomena exhibiting memory and hereditary properties, which cannot be captured by classical integer-order models. Solving fractional boundary value problems (FBVPs) is a challenging task, particularly due to the non-local natur...

This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species growth, and a system of parabolic partial differential equations describing the substrate dynamics. The free b...

In this article, we examine two problems: a fractional Sturm-Liouville boundary value problem on a compact star graph and a fractional Sturm-Liouville transmission problem on a compact metric graph, where the orders {\alpha }_{i} of the fractional derivatives on the ith edge lie in (0,1) . Our main objective is to introduce quantum graph Hamiltonia...

We obtain Riesz transform bounds and characterise operator-adapted Hardy spaces to solve boundary value problems for singular Schr\"odinger equations $-\mathrm{div}(A\nabla u)+aVu=0$ in the upper half-space $\mathbb{R}^{1+n}_{+}$ with boundary dimension $n\geq 3$. The coefficients $(A,a,V)$ are assumed to be independent of the transversal direction...

Solving systems of partial differential equations (PDEs) is a fundamental task in computational science, traditionally addressed by numerical solvers. Recent advancements have introduced neural operators and physics-informed neural networks (PINNs) to tackle PDEs, achieving reduced computational costs at the expense of solution quality and accuracy...

The focus of this paper is the investigation of a particular type of nonlinear deformable fractional differential equations, and analyzing their existence results. Our approach involves utilizing relevant fixed point theorems, we also explore the global convergence of successive approximations to provide additional insights into the topic. To furth...

In this article, the focus is on investigating the uniqueness, existence, and stability of a coupled system of fractional differential equations with non-separated coupled boundary conditions. The uniqueness of solutions for the presented problem is discussed by employing the fixed-point theorem. The Leray–Schauder’s alternative is used to investig...

Interfacial Dzyaloshinskii-Moriya interaction (IF-DMI) leads to non-collinear spin configurations within the magnetic layers of multilayer heterostructures, while its interlayer counterpart (IL-DMI) minimizes chiral states between the layers. Here, we demonstrate that the symmetries of these interactions are very different, even though both arise f...

We investigate the homogeneous Dirichlet boundary value problem for generalized Laplacian equations with a singular, potentially non-integrable weight. By examining asymptotic behaviors of the nonlinear term near 0 and ∞, we establish the existence, nonexistence, and multiplicity of positive solutions for all positive values of the parameter λ. Our...

In this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo sense, classical differential quadrature method, a...

The objective of this paper is to investigate a class of initial boundary value problems for inverse variational inequalities that arise from financial matters. By utilizing the energy inequality on a localized cylindrical region and the Caffarelli–Kohn–Nirenberge inequality, we establish the local boundedness and the Harnack inequality of weak sol...

A nonequilibrium thermodynamic model is presented for the nonisothermal lithium-ion battery cell. Coupling coefficients, all significant for transport of heat, mass, charge and chemical reaction, were used to model profiles of temperature, concentration and electric potential for each layer of the cell. Electrode surfaces were modelled with excess...

In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into an autoencoder architecture. This method’s integration of parametric space information significantly reduces the amount of training data needed to effectively p...

In this paper, we establish the existence and uniqueness of solutions for a system of coupled differential equations of arbitrary order subject to nonlinear boundary conditions within generalized Banach spaces. The fractional derivatives used are of Caputo-Fabrizio type. We provide the exact solution for an auxiliary boundary value problem and use...

Modeling of different processes and phenomena in real-world is one of the most important fields of the mathematics in which qualitative dynamics of such systems are studied from mathematical point of view. In this paper, we discuss the qualitative properties of solutions of a temperature control system in the context of a mathematical model in frac...

The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by numerical examples.

This paper investigates the degenerate non-local boundary value problem of logistic type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{ \begin{array}{l} -\Del...

This paper focuses on two-point boundary value problems for autonomous second order nonlinear differential equations of the form y'' = f(y,y') which can represent many problems in physics and engineering. Analytical integration of such equations leads to an indefinite integral, which in most cases cannot be expressed by elementary functions. In add...

The minimal operators generated by overdetermined boundary value problems for differential equations are extremely important in the description of regular boundary value problems for differential equations, and are also widely used in the study of local properties of solutions. The study of overdetermined boundary value problems is closely related...

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called Φs functions in the b-metric space to the extended b-metric space and the cone b-metric space, we introduce the class of ΦM functions and a...

This paper investigates the initial boundary value problem of finitely degenerate semilinear pseudo-parabolic equations associated with H\"{o}rmander's operator. For the low and critical initial energies, based on the global existence of solutions in the previous literature, we investigate the exponential decay estimate of the energy functional. Mo...

A fully parabolic chemotaxis model of Keller-Segel type with local sensing is considered. The system features a signal-dependent asymptotically non-degenerate motility function, which accounts for a repulsion-dominated chemotaxis. Global boundedness of classical solutions is proved for an initial Neumann boundary value problem of the system in any...

This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically condu...

This paper considers some initial boundary value problems for the heat equation in a bounded segment with a piecewise constant coefficient. Using the method of separation of variables, the problem under consideration is reduced to a spectral problem and eigenvalues and eigenfunctions of the resulting spectral problem are found. It is shown that the...

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages special splitting and interpolation schemes, providing iterative algorithm with a large degree of parallelizatio...

This study examined the fractional boundary value issue at flexible derivatives, focusing on establishing the existence of solutions and uniqueness. We introduce conditions that advance our understanding of this complex mathematical domain by capitalizing on the innovative framework of contraction principles. Moreover, the versatility of the propos...

This paper presents an analytical framework for in-plane two-impulse transfers between two Lissajous orbits around a single collinear libration point in the linearized circular restricted three-body problem. Based on the categorization of orbits near a collinear libration point in the linearized dynamics, we formulate two-impulse transfers as a two...

This study investigates the electromagnetic field (EMF) distribution of an ideal circular parallel plate capacitor excited by a time-harmonic power source. Considering the lead wire and capacitor as a charged whole, we formulate the boundary value problems of the Helmholtz equation for the EMF in the lead wire space and capacitor space, respectivel...

The purpose of the study is to investigate the thermal proficiency of a trihybrid magnetized water-based cross nanofluid over an inclined shrinking sheet. Cross-fluid is the best model to investigate the fluid flow at a very high and very low share rate. There are three nanoparticles that are added in based fluid (water) to form the requisite posit...

This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gra...

This study is a follow-up of two our papers (Appl. Math. Lett. 126 (2022) and MCMA 29:4 (2023)), where we developed a vector randomized algorithms with iterative refinement for large system of linear algebraic equations. We focus in this paper on the application of the vector randomized iterative refinement algorithm to boundary integral equations...

We consider a nonlinear Robin problem driven by the anisotropic (p, q)-Laplacian plus an indefinite potential term. In the reaction, we have the competing effects of a parametric concave (sublinear) term perturbed by a superlinear one (concave-convex problem). We prove the existence and multiplicity result for positive solutions which is global wit...

We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setle...

This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling contexts, where an exact solution is often unfeasible due to the intrinsic complexity of these equations. Thu...

Dielectric elastomers are increasingly studied for their potential in soft robotics, actuators, and haptic devices. Under time-dependent loading, they dissipate energy via viscous deformation and friction in electric polarization. However, most constitutive models and finite element (FE) implementations consider only mechanical dissipation because...

This paper presents an efficient wavelet collocation method that utilizes linear Legendre multi-wavelets. Linear Legendre multi-wavelets are introduced as a new family of orthogonal wavelets constructed from Legendre polynomials. These wavelets possess desirable properties, including compact support, vanishing moments, and symmetry. The multi-resol...

In this paper, a 3D Numerical Wave Tank (NWT) implementing a simplified version of the Mixed Eulerian–Lagrangian (MEL) scheme is developed to simulate large amplitude ship motion at a constant forward speed. A lower-order panel method within the framework of potential flow theory is used to calculate the velocity potential and its spatial derivativ...

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs inc...

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear nonlocal integro-differential p-Lévy operators. A prototypical example of integro-differential p-Lévy operators is the well-known fractional p-Laplace operator. Our main focus is on nonlinear integro-differential equations in the presence of...

In this paper, the finite element method (FEM) is integrated with orthogonal polynomial approximation in high-dimensional spaces to innovatively model the Moon’s surface gravity anomaly. The aim is to approximate solutions to Laplace’s classical differential equations of gravity, employing classical Chebyshev polynomials as basis functions. Using c...

Within this manuscript, we present an innovative concept of contraction, building upon the foundation laid by Jleli and Samet. Subsequently, we introduce the concept of θ-contractions. Leveraging these novel ideas, we formulate a series of fresh fixed-point theorems applicable to spaces utilizing the Controlled Branciari metric. Notably, our approa...

For 3-D quadratically quasilinear wave equations with or without null conditions in exterior domains, when the compatible initial data and Dirichlet boundary values are given, the global existence or the optimal existence time of small data smooth solutions have been established in early references. However, for 2-D quadratically quasilinear wave e...

We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a neighborhood of the boundary, we establish log-type stability estimates for these perturbations from a partial Dirichl...

This study presents a symbolic approach for solving second order boundary value problems with Stieltjes boundary conditions (integral, differential, and generic boundary conditions). The proposed symbolic method computes the Green's operator and the Green's function of the provided boundary value problem on the level of operators by applying the al...

In this work, we study the existence and multiplicity of solutions to the problem $$\displaylines{ -(\Delta)_p^s u + V(x)|u|^{p-2}u = \lambda f(u),\quad x\in\Omega;\cr u=0,\quad x\in \mathbb{R}^N\backslash\Omega, }$$ where \(\Omega\subset\mathbb{R}^N\) is an open bounded set with Lipschitz boundary \(\partial\Omega\), \(N\geqslant 2\), \(V\in L^{\i...

In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global Maxwellian with nonzero macroscopic velocities at the far field. We first explicitly address the sound speed for the...

The aim of this paper is to obtain a fractal set of −iteratedfunctionsystemscomprisinggeneralized-contractions. For a variety of Hutchinson–Wardowski contractive operators, we prove that this kind of system admits a unique common attractor. Consequently, diverse outcomes are obtained for generalized iterated function systems satisfying various gene...

The focus of this study is on boundary-value issues for Caputo-type fractional differential equations of order 1 < q < 2. To begin, we demonstrate the existence theorem of mild solutions under certain lesser constraints combining the measure of non-compactness and Darbo's fixed-point theorem. The generalized Ulam-Hyers stability requirements are th...

In this paper, we consider the incompressible 3D Euler and Navier–Stokes equations in a smooth bounded domain. First, we study the 3D Euler equations endowed with slip boundary conditions and we prove the same criteria for energy conservation involving the gradient, already known for the Navier–Stokes equations. Subsequently, we utilize this findin...

In this paper, we propose a new numerical method to simulate acoustic scattering problems in two‐dimensional periodic structures with non‐periodic incident fields. Applying the Floquet‐Bloch transform to the scattering problem yields a family of quasi‐periodic boundary value problems dependent on the Floquet‐Bloch parameter. Consequently, the solut...

In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic equation with a drift $b\in L_2$. We prove $L_1$-stability of solutions with respect to perturbations of the drift $b$ in $L_2$ in the case if the drift satisfies the ``n...

The study of finite size stress concentration in the design and implementation of piezoelectric semiconductor devices is crucial. A symmetric collinear cracks model is established for piezoelectric semiconductor with finite thickness dimensions. Considering two boundary conditions of stress and displacement, the dislocation density functions are in...

Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity conditions, also obey the Kirchhoff conditions, expressing the balance of tensions. In this paper, we propose a n...

We investigate the qualitative properties of weak solutions to the boundary value problems for fourth-order linear hyperbolic equations with constant coefficients in a plane bounded domain convex with respect to characteristics. Our main scope is to prove some analog of the maximum principle, solvability, uniqueness and regularity results for weak...

In this paper, we prove existence results for entropy solutions of a nonlinear boundary value problems represented by a class of nonlinear elliptic anisotropic equations with variable exponents and natural growth terms. The functional setting involves variable exponents anisotropic Sobolev spaces.

This paper proposes a method for topology optimization of link mechanisms with multiple outputs, using a multi-material micropolar elasticity model. This approach allows for comprehensive optimization of both the arrangement and structure of the link mechanism components. By utilizing a continuum model that incorporates micropolar elasticity, we ca...