We present an implementation of Böhmer’s finite element method for fully nonlinear elliptic partial differential equations on convex polygonal domains, based on a modified Argyris element and BernsteinBézier techniques. Our numerical experiments for several test problems, involving the classical Monge-Ampère equation and an unconditionally elliptic equation, confirm the convergence and error bo...

1. Introduction The stationary behaviour of semiconductor devices is governed by a set of nonlinear elliptic partial differential equations. This includes a nonlinear Poisson equation and two nonlinear continuity equations. Using Gummel's method [2] we can decouple the nonlinear elliptic system so that at each step we solve an equation of the form

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equa...

Kudryashov in [ Phys. Lett. A 342 (2005) 99-106] used simplest nonlinear differential equations like the Riccati equation, the equation for the Jacobi elliptic function to present a new approach for searching exact solutions of nonlinear partial differential equations. As application, he obtained a kind of exact solutions to the Fisher equation. In this letter, more explicit exact solitary wave...

In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the biparabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the present paper some boundary-value problems with non-local initial condition for model and degenerate parabol...

By using solutions of an ordinary differential equation, an auxiliary equationmethod is described to seek exact solutions of variablecoefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for...

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm altern...