Title:Uniform boundedness and eventual Hölder continuity to a cancer invasion model with porous medium diffusion
Speaker:Chunhua Jin（South China Normal University）
Time:Friday, April 12, 2024, 09:30-11:30
Location：Tecent meeting, Meeting ID：482 982 217, Password：190101
Abstract：This talk focuses on a specific class of cancer invasion models that incorporate ECM remodeling and nonlinear diffusion. Unfortunately, the well-coupled structure between the diffusion term and the haptotactic term is destroyed, making the effective methods used in linear diffusion models no longer applicable. We constructed a new functional that can offset the inherent difficulties caused by the low regularity of the haptotactic term, thus improving the regularity of weak solutions. Based on these results, we can prove part of long-time asymptotic behavior of the solution, thereby finally proving the uniform boundedness of the weak solution. Subsequently, by improving the convergence of cancer cells $u$ from $L^p$-norm to $L^\infty$-norm, it is also proved that after a long time, the weak solution will eventually be Hölder continuous for some slow diffusion cases.
