Global well-posedness and eventual Holder continuity to a cancer invasion model with remodelling of ECM and nonlinear diffusion
报告地点： 线上会议（腾讯会议号： 167-449-279）
内容简介： This talk is concerned with a class of cancer invasion model with remodeling of ECM. The simultaneous occurrence of remodeling effect and nonlinear diffusion brings essential difficulties to the estimation of uniform boundedness of solutions, although the global existence of solutions is easy to obtain. We use some new techniques to improve the regularity of the solution, and obtain partial large time behavior of the solution. Using this, we further obtain the uniform boundedness of the solution, and finally determine the long-term asymptotic behavior of the solution. Subsequently, by improving the convergence of cancer cells $u$ from $L^p$-norm to $L^\infty$-norm, it is proved that after a long time, the weak solution will eventually H\"older continuous for some slow diffusion cases.
报告人简介： 金春花，华南师范大学教授。 2013年入选教育部新世纪优秀人才支持计划，主持了包括国家自然科学基金面上项目, 广东省杰出青年基金项目等在内的多项研究课题。 主要从事非线性扩散模型相关理论的研究，近几年来研究兴趣主要集中在生物趋化相关模型解的适定性理论研究