Uniqueness of Solutions to a System of Differential Inclusions

Abstract

In this paper we study the uniqueness of solutions to the initial and Dirichlet boundary-value problem of differential inclusions ∆ui + ∇∙ B→i (u1, u2,...,uN) ∈ ∂Fi(ui)/ ∂t, i = 1,2,...,N, where B→i (s1, s2,..., sN) is an n-dimensional vector continuously differentiable on ℝN, and Fi(ui) = {wi : ui = Ai(wi)}, i = 1,2,...,N with Ai(s) continuously differentiable functions on ℝ and A'i(s) ≥ 0.