## About

58

Publications

4,418

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

406

Citations

Citations since 2017

## Publications

Publications (58)

The main goal of this paper is to introduce and analyze a new nonlocal reaction-diffusion model with in-homogeneous Neumann boundary conditions. We prove the existence and uniqueness of a solution in the class \begin{document}$ C((0, T], L^\infty(\Omega)) $\end{document} and the dependence on the data. Proofs are based on the Banach fixed-point the...

The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy–Stefan–Boltzmann boundary conditions, extending the types already studied. Under certain assumptions, we prove the existence, a priori estimates, regularity and uniqueness of a solution in the class Wp1,2(Q). Here we...

In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on the input data: f(t,x), w(t,x) an...

Ebook available free of charge at
https://www.aimsciences.org/book/deds/volume/Volume%207

The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy–Neumann boundary conditions, extending the types already studied. Under some certain assumptions, we prove the existence, estimate, regularity and uniqueness of a classical solution. The considered nonlinear second-or...

The paper concerns with an implicit first-order in time, finite-differences in space, method to solve numerically a reaction-diffusion equation endowed with a cubic nonlinearity, and non-homogeneous Neumann boundary conditions. Numerical tests for the Allen-Cahn equation are presented and analyzed in terms of the physical quantities of interest.

A novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced first, then the corresponding Euler-Lagrange equation being determined. A nonlinear parabolic PDE model is then obtained from this equation. It is based on a novel edge-stopping function and...

We present the error analysis of three time-stepping schemes used in the discretization of a nonlinear reaction-diffusion equation with Neumann boundary conditions, relevant in phase transition. We prove L∞ stability by maximum principle arguments, and derive error estimates using energy methods for the implicit Euler, and two implicit-explicit app...

This work is devoted to the study of a phase-field transition system of Caginalp type endowed with a general polynomial nonlinearity and a general class of nonlinear and nonhomogeneous dynamic boundary conditions (in both unknown functions). The existence, uniqueness and regularity of solutions are established. Here we extend several results proved...

This paper is concerned with an optimal control problem (P) (both distributed control as well as boundary control) for the nonlinear phase-field (Allen-Cahn) equation, involving a regular potential and dynamic boundary conditions. A family of approximate optimal control problems (Pϵ) is introduced and results for the existence of an optimal control...

The evolution of surface relief characteristics of stress induced martensite plates was investigated at Fe-Mn-Si-Cr, Fe-Mn-Si-Cr-Ni and Cu-Al-Ni shape memory alloys (SMAs), subjected to tensile deformation. Hot-rolled specimens underwent different successive stages of pre-straining, by means of a tensile testing machine, at room temperature (RT). T...

The paper is concerned with the numerical analysis of a scheme of fractional steps type, associated to the nonlinear phase-field (Allen- Cahn) equation, endowed with non-homogeneous dynamic boundary conditions (depending both on the time and space variables). To approximate the solution of the linear parabolic equation, introduced by such approxima...

This paper is devoted to the study of a Caginalp phase-field system endowed with non-homogeneous Cauchy-Neumann and nonlinear dynamic boundary conditions. We first prove the existence, uniqueness and regularity of solutions to an Allen-Cahn equation. Our approach allows to consider in the dynamic boundary conditions a nonlinearity of higher order t...

In this work we model and analyze two control strategies to diminish a pest population using traps. The action of any trap depends on its age. Both problems contain bilinear control rates. The large-time behavior of the model with time-periodic inflow is investigated. The first control strategy deals with a finite horizon problem while the second o...

This paper studies a Caginalp phase-field transition system endowed with a general regular potential, as well as a general class, in both unknown functions, of nonlinear and non-homogeneous (depending on time and space variables) boundary conditions. We first prove the existence, uniqueness and regularity of solutions to the Allen–Cahn equation, su...

Lamellar specimens of Cu-Zn-Al Shape Memory Alloy (SMA) were trained in bending under as much as 500 cycles, until two-way shape memory effect (2WE) was obtained. Trained specimens were further tested by means of a hydraulic installation where, heating-cooling cycles were performed in oil conditions. Considering that the lower concave surface of th...

The paper is mainly concerned with numerical approximation of solutions to the phase-field transition system (Caginalp's model), subject to the non-homogeneous Dirichlet boundary conditions. Numerical approximation of solutions to the nonlinear phase-field (Allen-Cahn) equation, supplied with the non-homogeneous Dirichlet boundary conditions as wel...

The paper establishes the existence, estimate, uniqueness and regularity for the solution of a nonlinear parabolic system (a two-phase Caginalp type system) with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity. It extends the already studied types of boundary conditions which...

A scheme of fractional steps type, associated to the nonlinear phase-field transition system in one dimension, is considered in this paper. To approximate the solution of the linear parabolic system introduced by such approximating scheme, we consider three finite differences schemes: 1-IMBDF (first-order IMplicit Backward Differentiation Formula),...

Last years have shown a great interest in studying applied mathematics problems. One of the most important classes of such problems is the class of systems with phase change (systems with free boundary) encountered in numerous problems of physics, such as: melting ice, crystal formation, diffusion of oxygen in an absorbent tissue, solidification in...

In this paper we prove the convergence of an iterative scheme of fractional steps type for a non-homogeneous Cauchy-Neumann
boundary optimal control problem governed by non-linear phase-field system, when the boundary control is dependent both on
time and spatial variables. Moreover, necessary optimality conditions are established for the approxima...

The paper establishes existence, uniqueness and regularity for the solution of a phase-field transition system with non-homogeneous
Cauchy-Neumann boundary conditions. Moreover, some estimates for the solution are given. The non-linear parabolic problem
considered here can be used to modeling the solidification (liquidification) process to a matter...

In this paper we study an inverse problem, in one space dimension case, connected with the industrial solidification process called casting wire, as an optimal control problem governed by nonlinear phase-field system with nonhomogeneous Cauchy–Neumann boundary conditions. We prove the convergence of an iterative scheme of fractional steps type for...

The inverse problem, denoted by (P), in 2D space dimension governed by the nonlinear parabolic system (the phase-field transition system, introduced by G. Caginalp [Arch. Ration. Mech. Anal. 92, 205–245 (1986; Zbl 0608.35080)]), is considered. For every ε>0, we associate to the nonlinear system an approximating scheme of fractional steps type; corr...

The paper presents a proof of the convergence for an iterative scheme of fractional steps type associated to the phase-field transition system (a nonlinear parabolic system) with non-homogeneous Cauchy–Neumann boundary conditions. The advantage of such method consists in simplifying the numerical computation necessary to be done in order to approxi...

The main goal of this article is to present some applications of a new numerical model to the continuous casting process. Industrial implementation of the software package developed in this context was made to the secondary cooling zone of a continuous casting machine at ArcelorMittal Steel S. A. Galati

The phase field transition system (a nonlinear system of parabolic type) introduced by Caginalp [6] to distinguish between the phases of the material that is involved in the solidification process is considered. On the basis of the convergence of an iterative scheme of fractional steps type, a numerical algorithm is constructed in order to approxim...

The main goal of this article is to present some applications of a new numerical model to the continuous casting process. Industrial implementation of the software package developed in this context was made to the secondary cooling zone of a continuous casting machine at ArcelorMittal Steel S. A. Galati.

The phase field transition system (a nonlinear system of parabolic type) introduced by Caginalp to distinguish between the phases of the material that is in¬volved in the solidification process is considered. On the basis of the convergence of an iterative scheme of fractional steps type, a numerical algorithm is constructed in order to approximate...

The phase field transition system (a nonlinear system of parabolic type) introduced by Caginalp to distinguish between the phases of the material that is involved in the solidification process is considered. On the basis of the convergence of an iterative scheme of fractional steps type, a numerical algorithm is constructed in order to approximate...

This paper deals with the existence and necessary optimality conditions for an optimal control problem governed by a phase-field transition system. The one-point boundary (time variable) state condition is considered. A numerical algorithm of gradient type and numerical implementation are reported, too.

The 2D phase field transition system introduced by G. Caginalp to distinguish between the phases of the material that is involved in the solidification process is considered. On the basis of the convergence of an iterative scheme of fractional steps type, a numerical algorithm is constructed. The advantages of such approach is that the new method s...

Elemente de bază ale sistemului de operare Linux; Sisteme de fişiere în Linux; Prelucrarea fişierelor text; Procese şi gestiunea memoriei; Programare sub shell-ul bash; Reţele de calculatoare; Pachete de programe; Instalarea distribuţiei Linux Mandrake; Sistemul de management al fişierelor; Resurse Linux pe Internet.

In this paper we prove the convergence of an iterative scheme of
fractional steps type for boundary optimal control problem
which is governed by the phase--field transition system.
The existence of an optimal control and necessary optimality
conditions are given for approximating problem. A gradient type
algorithm and numerical implementation of...

The paper establishes the product formula for semi-groups of nonlinear operators on a real Hilbert space in the case where one of the operators is ω-m-accretive. This extends a well-known result for maximal monotone operators (the case ω = 0). An example dealing with Caginalp's model is given.

This work is concerned with an approximation process for the identification of nonlinearities in the
nonlinear periodic wave equation. It is based on the least-square approach and on a splitting method.
A numerical algorithm of gradient type and the numerical implementation are given.

We prove the convergence of an iterative scheme of fractional steps type for the nonlinear Riccati equation. The use of this method simplifies the numerical algorithms due to its decoupling feature. A numerical algorithm and numerical results are presented.

Many algorithms were elaborated for minimizing the costs necessary to perform a single, isolated query in a distributed database system. A distributed system can receive different types of queries and processes them at the same time. In this case the determination of the optimal query processing strategy is a stochastic optimization problem. Query...

The paper studies a nonlinear parabolic system extending various significant phase-field models. One proves the existence, the estimate and the uniqueness of the solution. Our approach allows to consider a nonlinearity of higher-order than in the known results.

The existence, the estimate, and the uniqueness of a solution to a general phase-field system, motivated by Caginalp's model describing the phase changes, are established. The paper extends the results for the already studied types of nonlinearities related to the model.

The ID phase-field transition system introduced by Caginalp to describe the moving boundary in melting problems is considered. It is discretized by finite differences and three algorithms are presented to solve the resulting nonlinear algebraic system: the Newton method, an improved Newton method with reduced system and a fractional step method. Nu...

The 1D phase-field transition system introduced by Caginalp to
describe the moving boundary in melting problems is considered.
It is discretized by finite differences and three algorithms are presented to solve
the resulting nonlinear algebraic system : the Newton method, an improved
Newton method with reduced system and a fractional step method...

The inverse phase transition problem in one space dimension with flux boundary conditions is considered. The problem is treated via a new method introduced by V. Barbu [Control of phase transition (to appear)]. We present the optimal control problem, establish the necessary optimality conditions and derive a descent algorithm. Some numerical result...

## Projects

Projects (3)

Special Issue of "Advances in Mathematical Physics", Hindawi
Call for Papers:
https://www.hindawi.com/journals/amp/si/626404/cfp

Lead Guest Editor
Dr. Habil. Tudor Barbu, Institute of Computer Science of the Romanian Academy, Iaşi, Romania
tudor.barbu@iit.academiaromana-is.ro
Guest Editors
Gabriela Marinoschi, Institute of Mathematical Statistics and Applied
Mathematics of the Romanian Academy (ISMMA), Bucharest, Romania
gabimarinoschi@yahoo.com
Costică Moroşanu, “Al. I. Cuza” University, Iaşi, Romania
costica.morosanu@uaic.ro
Ionuţ Munteanu, Bielefeld University, Bielefeld, Germany
jmunteanu@math.uni-bielefeld.de
Submission Deadline
Friday, 24 November 2017
Publication Date
April 2018
The objective of this special issue of the journal is to disseminate advanced research in these domains and to bring together the research achievements of scientists in the PDE based image processing areas, so as to extend the existing knowledge in these fields. Therefore, we encourage the authors to contribute original high-quality manuscripts that describe novel theoretical and practical results on relevant topics, as well as review articles describing the current state of the art.
Potential topics include but are not limited to the following:
Novel PDE variational image restoration solutions using second-and fourth-order diffusion models
Nonlinear anisotropic diffusion schemes for image boundary detection Advanced second-and higher-order PDE-based imagei nterpolation techniques
Partial differential equation-based compression and decompression approaches
Variational level-set based frameworks for image segmentation Effective variational PDE models for optical flow computation Computational techniques for nonlinear image registration using variational solutions
Rigorous mathematical investigation of these PDE-based models and their numerical approximation schemes:well-posedness, stability, convergence, and consistency
Hybrid denoising and restoration methods involving nonlinear PDE filters
Authors can submit their manuscripts through the Manuscript Tracking System at https://mts.hindawi.com/submit/journals/mpe/avpde/.

A book is in progress now om this topic. It contains eigenvalue problems, t. p. b. v. p. and p. d. e. defined on the half line and on the real axis.