Electron. J. Diff. Eqns., Vol. 2000(2000), No. 43, pp. 1-8.

Uniqueness of solutions to a system of differential inclusions

Chunpeng Wang & Jingxue Yin

Abstract:
In this paper we study the uniqueness of solutions to the initial and Dirichlet boundary-value problem of differential inclusions
$$ \Delta u_i+\nabla\cdot\vec{B_i} (u_1,u_2,\dots,u_N)\in \frac{\partial F_i(u_i)}{\partial t}, \quad i=1,2,\dots,N, $$
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.

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Chunpeng Wang
Department of Mathematics
JiLin University
Changchun, Jilin 130023, People's Republic of China
Jingxue Yin
Department of Mathematics
JiLin University
Changchun, Jilin 130023, People's Republic of China
e-mail: yjx@mail.jlu.edu.cn

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