红楼Y论坛（第六十七讲）-A degeneration volume-filling model with different diffusivity constants

红楼Y论坛（第六十七讲）

Topic: A degeneration volume-filling model with different diffusivity constants

Time：15:00-16:00  May.10, 2023（Wednesday）

Place：Room457，Haiqin No.2

Speaker：Ling Liu

Abstract：The existence of a weak solution to a degenerate cross-diffusion system with different diffusivity constants is shown. We have also shown the weak solution converges strongly in $L^2$-norm as time approaches infinity. We mainly focus on the matrix analysis in the existence proof, with the rest part largely rely on previous work. By analyzing a pair of delicate ``quasi" relative entropies we have constructed, with applications of logarithmic convex inequalities, we obtain the convergence results for relative entropies, then we are able to derive the large time behavior result.