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.