On the Role of Diffusion Behaviors in Stability Criterion forp-Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value

Abstract

By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev spaceW01,p(Ω), a global asymptotical stability criterion forp-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinearp-Laplace diffusion item plays its role in the new criterion though the nonlinearp-Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.