We study a generalization of the fully overdamped Frenkel-Kontorova model in dimension n ≥ 1. This model describes the evolution of the position of each atom in a crystal, and is mathematically given by an infinite system of coupled first order ODEs. We prove that for a suitable rescaling of this model, the solution converges to the solution of a Peierls-Nabarro model, which is a coupled system...

This paper deals with the null-controllability of a system mixed parabolic-elliptic pdes at any given time T>0. More precisely, we consider Kuramoto-Sivashinsky–Korteweg-de Vries equation coupled second order elliptic posed in interval (0,1). We first show that linearized is globally null-controllable by means localized interior control acting on either KS-KdV or equation. Using Carleman approa...

A two-dimensional unstructured elliptic smoothing method is described where the Winslow equations are discretized using a finite volume approach. Virtual control volumes for each node are constructed with element shapes that are nearly ideal. Green-Gauss theorem is used to formulate gradients over an element or a collection of elements for a node, which ultimately leads to a coupled non-linear ...

We study a system of elliptic equations from the Abelian BornInfeld system coupled with the Einstein equations under the boundary condition of the symmetric vacuum(nontopological type). When the total string number satisfies 1 ≤ N < 1 4πG , where G is the gravitational constant, we construct a family of solutions to the system. The qualitative properties of the solutions are quite different fro...

In our work the phenomena determining the performance of semiconductor devices are examined. We use computer simulations based on semi-classical drift-diffusion model. Our aim is to numerically solve a system of three nonlinear elliptic differential equations. For computations, we use a coupled Newton method, with a modification taking advantage of a simple iteration.

We study a seawater intrusion problem in a confined aquifer. This process can be formulated as a coupled system of partial differential equations which includes an elliptic and a degenerate parabolic equation. Existence results of weak solutions, under realistic assumptions, are established through time discretization combined with parabolic regularization.

The theory of maximal monotone operators is utilized to prove the existence of weak periodic solutions for a coupled nonlinear parabolic-elliptic system.The diffusion term in the parabolic equation contains a Leray-Lions operator.This system may be regarded as a generalized version of the evolution thermistor model.

In this paper we study local higher regularity properties of a linear elliptic system that is coupled with Maxwell-type. The result proved by means modified finite difference argument. These differences are based on inner variations combined Piola-type transformation in order to preserve the curl-structure Maxwell system. applied relaxed micromorphic model.