Stability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion

Abstract

We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values.

Keywords

• stability
• nonlinear parabolic problem
• nonstandard growth
• cross-diffusion