# Nonlinear Differential Equations and Applications NoDEA (NODEA-NONLINEAR DIFF )

Publisher: Springer Verlag

## Description

The purpose of the Journal NoDEA - Nonlinear Differential Equations and Applications - is to encourage the interaction between pure mathematics and applied sciences. In particular it will provide a forum for research papers on nonlinear differential equations and applications to natural sciences. General theory will include ordinary and partial differential equations (both deterministic and stochastic) variational and topological methods control theory qualitative analysis including stability and bifurcation. Applications to natural sciences include the treatment of problems in classical statistical and quantum mechanics electromagnetism population dynamics chemical kinetics combustion theory.

• Impact factor
0.67
Show impact factor history

Impact factor
.
Year
• 5-year impact
0.92
• Cited half-life
5.70
• Immediacy index
0.11
• Eigenfactor
0.00
• Article influence
0.88
• Website
Nonlinear Differential Equations and Applications website
• Other titles
Nonlinear differential equations and applications (Online), NoDEA
• ISSN
1021-9722
• OCLC
43346736
• Material type
Document, Periodical, Internet resource
• Document type
Internet Resource, Computer File, Journal / Magazine / Newspaper

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author can archive a post-print version
• Conditions
• Authors own final version only can be archived
• Publisher's version/PDF cannot be used
• On author's website or institutional repository
• On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
• Published source must be acknowledged
• Must link to publisher version
• Set phrase to accompany link to published version (The original publication is available at www.springerlink.com)
• Articles in some journals can be made Open Access on payment of additional charge
• Classification
​ green

## Publications in this journal

• ##### Article: An approximation scheme for the anisotropic and nonlocal mean curvature flow
[hide abstract]
ABSTRACT: In 2004 Chambolle proposed an algorithm for mean curvature flow based on a variational problem. Since then, the convergence, extensions and applications of his algorithm have been studied by many people. In this paper we give a proof of the convergence of an anisotropic version of Chambolle’s algorithm by use of the signed distance function. An application of our scheme to an approximation of the nonlocal curvature flow such as crystalline one is also discussed.
Nonlinear Differential Equations and Applications NoDEA 04/2014; 21(2).
• ##### Article: Infinite speed of support propagation for the Derrida–Lebowitz–Speer–Spohn equation and quantum drift–diffusion models
[hide abstract]
ABSTRACT: We show that weak solutions of the Derrida–Lebowitz–Speer–Spohn (DLSS) equation display infinite speed of support propagation. We apply our method to the case of the quantum drift–diffusion equation which augments the DLSS equation with a drift term and possibly a second-order diffusion term. The proof is accomplished using weighted entropy estimates, Hardy’s inequality and a family of singular weight functions to derive a differential inequality; the differential inequality shows exponential growth of the weighted entropy, with the growth constant blowing up very fast as the singularity of the weight becomes sharper. To the best of our knowledge, this is the first example of a nonnegativity-preserving higher-order parabolic equation displaying infinite speed of support propagation.
Nonlinear Differential Equations and Applications NoDEA 02/2014;
• ##### Article: {W^{1,1}_0} -solutions for elliptic problems having gradient quadratic lower order terms
[hide abstract]
ABSTRACT: In this paper we deal with solutions of problems of the type $$\left\{\begin{array}{ll}-{\rm div} \Big(\frac{a(x)Du}{(1+|u|)^2} \Big)+u = \frac{b(x)|Du|^2}{(1+|u|)^3} +f \quad &{\rm in} \, \Omega,\\ u=0 &{\rm on} \partial \, \Omega, \end{array} \right.$$ where ${0 < \alpha \leq a(x) \leq \beta, |b(x)| \leq \gamma, \gamma > 0, f \in L^2 (\Omega)}$ and Ω is a bounded subset of ${\mathbb{R}^N}$ with N ≥ 3. We prove the existence of at least one solution for such a problem in the space ${W_{0}^{1, 1}(\Omega) \cap L^{2}(\Omega)}$ if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: $$J (v) = \frac{\alpha}{2} \int_{\Omega}\frac{|D v|^2}{(1 + |v|)^{2}} + \frac{12}{\int_{\Omega}|v|^2} - \int_{\Omega}f\,v , \quad f \in L^2(\Omega),$$ where in this case a(x) ≡ b(x) = α > 0.
Nonlinear Differential Equations and Applications NoDEA 12/2013;
• ##### Article: Symplectic and contact properties of the Ma\~n\'e critical value of the universal cover
[hide abstract]
ABSTRACT: We discuss several symplectic aspects related to the Ma\~n\'e critical value c_u of the universal cover of a Tonelli Hamiltonian. In particular we show that the critical energy level is never of virtual contact type for manifolds of dimension greater than or equal to three. We also show the symplectic invariance of the finiteness of the Peierls barrier and the Aubry set of the universal cover. We also provide an example where c_u coincides with the infimum of Mather's \alpha -function but the Aubry set of the universal cover is empty and the Peierls barrier is finite. A second example exhibits all the ergodic invariant minimizing measures with zero homotopy, showing that the union of their supports is not a graph, in contrast with Mather's celebrated graph theorem.
Nonlinear Differential Equations and Applications NoDEA 09/2013;
• Source
##### Article: Asymptotic Analysis of a Non-Linear Non-Local Integro-Differential Equation Arising from Bosonic Quantum Field Dynamics
[hide abstract]
ABSTRACT: We introduce a one parameter family of non-linear, non-local integro-differential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of the solutions of the one parameter family towards the solution of the limit equation.
Nonlinear Differential Equations and Applications NoDEA 12/2012;
• Source
##### Article: On $C^{1+\alpha}$ regularity of solutions of Isaacs parabolic equations with VMO coefficients
[hide abstract]
ABSTRACT: We prove that boundary value problems for fully nonlinear second-order parabolic equations admit $L_{p}$-viscosity solutions, which are in $C^{1+\alpha}$ for an $\alpha\in(0,1)$. The equations have a special structure that the "main" part containing only second-order derivatives is given by a positive homogeneous function of second-order derivatives and as a function of independent variables it is measurable in the time variable and, so to speak, VMO in spatial variables.
Nonlinear Differential Equations and Applications NoDEA 11/2012;
• ##### Article: A condition guaranteeing the absence of the blow-up phenomenon for the generalized Burgers equation
[hide abstract]
ABSTRACT: The initial boundary value problem for the generalized Burgers equation with nonlinear sources is considered. We formulate a condition guaranteeing the absence of the blow-up of a solution and discuss the optimality of this condition.
Nonlinear Differential Equations and Applications NoDEA 09/2012; 75(13):5119–5122.
• Source
##### Article: On the stability of travelling waves with vorticity obtained by minimisation
[hide abstract]
ABSTRACT: We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.
Nonlinear Differential Equations and Applications NoDEA 07/2012;
• ##### Article: The Cauchy problem for the integrable Novikov equation
[hide abstract]
ABSTRACT: In this paper we consider the Cauchy problem for the integrable Novikov equation. By using the Littlewood–Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the integrable Novikov equation is locally well-posed in the Besov space Bp,rs with 1⩽p,r⩽+∞1⩽p,r⩽+∞ and s>max{1+1p,32}. In particular, when u0∈Bp,rs∩H1 with 1⩽p,r⩽+∞1⩽p,r⩽+∞ and s>max{1+1p,32}, for all t∈[0,T]t∈[0,T], we have that ‖u(t)‖H1=‖u0‖H1‖u(t)‖H1=‖u0‖H1. We also prove that the local well-posedness of the Cauchy problem for the Novikov equation fails in B2,∞3/2.
Nonlinear Differential Equations and Applications NoDEA 07/2012; 253(1):298–318.
• Source
##### Article: Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations
[hide abstract]
ABSTRACT: We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We prove a one-to-one relation between the long time behavior of the solution and the limit value of its energy for symmetric decreasing initial data in $L^2$ under minimal assumptions on the nonlinearities. The obtained relation allows to establish sharp threshold results between propagation and extinction for monotone families of initial data in the considered general setting.
Nonlinear Differential Equations and Applications NoDEA 03/2012; 20(4).
• Source
##### Article: Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion
[hide abstract]
ABSTRACT: We obtain necessary and sufficient conditions for equivalence of law for linear stochastic evolution equations driven by a general Gaussian noise by identifying the suitable space of controls for the corresponding deterministic control problem. This result is applied to semilinear (reaction-diffusion) equations driven by a fractional Brownian motion. We establish the equivalence of continuous dependence of laws of solutions to semilinear equations on the initial datum in the topology of pointwise convergence of measures and null controllability for the corresponding deterministic control problem.
Nonlinear Differential Equations and Applications NoDEA 03/2012; 20(4).

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