一类退化拋物变分不等式问题解的存在性和唯一性

Existence and Uniqueness of Solutions to a Class of Degenerate Parabolic Variational Inequalities

本文研究了一类基于非线性抛物变分不等式问题， {min{Lu,u-u0}=0,（x,t）∈ΩT, u（x,0）=u0（x）,x∈Ω, u（x,t）=0,（x,t）∈ Ω×（0,T）,其中L表示变指数退化抛物算子．通过新的惩罚函数和微分不等式级数，证明了该变分不等式解的存在性和唯—性．

AIn this paper, we study the existence and uniqueness of solutions to the following kind of variational inequalities {min{Lu,u-u0}=0,（x,t）∈ΩT, u（x,0）=u0（x）,x∈Ω, u（x,t）=0,（x,t）∈ Ω×（0,T）,where L is a degenerate parabolic operators with variable uniqueness results for the above variational inequalities are function and differential inequality technique. exponent. The existence and obtained by some new penalty function and differential inequality technique.