Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 43, pp. 1-8.

Title: Uniqueness of solutions to a system of differential inclusions

Authors: Chunpeng Wang (JiLin Univ. Changchun, China)
 Jingxue  Yin (JiLin Univ. Changchun, China)
    
Abstract: 
 In this paper we study the uniqueness of solutions to
 the initial and Dirichlet boundary-value problem of
 differential inclusions
 $$
 \Delta u_i+\nabla\cdot\vec {B_i}
 (u_1,u_2,\dots,u_N)\in {\partial F_i(u_i) \over \partial t},
 \quad i=1,2,\dots,N,
 $$
 where $\vec{B_i}(s_1,s_2,\dots,s_N)$ is an
 $n$-dimensional vector continuously differentiable on ${\mathbb R}^N$,
 and $F_i(u_i)=\{w_i:u_i=A_i(w_i)\}$, $i=1,2,\dots,N$
 with $A_i(s)$ continuously differentiable functions on ${\mathbb R}$ and
 $A'_i(s)\geq 0$.
 
Submitted May 15, 2000. Published June 12, 2000. 
Math Subject Classifications: 35K50, 35K65, 35A05, 35D99.
Key Words: differential inclusions; degeneracy; uniqueness.