EXISTENCE AND UNIQUENESS OF SOLUTIONS OF DEGENERATE CHEMOTAXIS SYSTEM

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Existence and uniqueness of solutions for a semilinear elliptic system

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.

Existence and Uniqueness of Solutions to a Semilinear Elliptic System

In this article, we show the existence and uniqueness of smooth solutions for boundary-value problems of semilinear elliptic systems.

On Uniqueness and Existence of Entropy Solutions of Weakly Coupled Systems of Nonlinear Degenerate Parabolic Equations

We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori e...

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.