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

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.

Automated summary

This study investigates the stability of a unique weak solution to certain parabolic systems with nonstandard growth conditions and cross-diffusion terms, demonstrating that two unique weak solutions with different initial values are controlled by these initial values.