Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Concentrating solutions for an anisotropic elliptic problem with large exponent

We consider the following anisotropic boundary value problem ∇(a(x)∇u) + a(x)u = 0, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitraril...

Existence and Continuation of Solutions for a Nonlinear Neumann Problem

In this article we study the existence, continuation and bifurcation from infinity of nonconstant solutions for a nonlinear Neumann problem. We apply the LeraySchauder degree and the degree for SO(2)-equivariant gradient operators defined by the second author in [21].

Entropy Solutions for Nonlinear Degenerate Elliptic-parabolic-hyperbolic Problems

We consider the nonlinear degenerate elliptic-parabolic-hyperbolic equation ∂tg(u)−∆b(u)− div Φ(u) = f(g(u)) in (0, T )× Ω, where g and b are nondecreasing continuous functions, Φ is vectorial and continuous, and f is Lipschitz continuous. We prove the existence, comparison and uniqueness of entropy solutions for the associated initial-boundary-value problem where Ω is a bounded domain in RN . ...

Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem

Parallelization of the algebraic ctitious domain method is considered for solving Neumann boundary value problems with variable coeecients. The resulting method is applied to the parallel solution of the subsonic full potential ow problem which is linearized by the Newton method. Good scalability of the method is demonstrated in Cray T3E distributed memory parallel computer using MPI in communi...