Global Solvability and Stability Dominated by Chemotaxis in a PDE-ODE Model

讲座题目Title：Global Solvability and Stability Dominated by Chemotaxis in a PDE-ODE Model

讲座时间 Datetime: 2024.6.14  15:00-17:30

地点 Venue: 海琴2号楼A457

报告人 Speaker: 金春花 教授

单位 Affiliation: 华南师范大学

主持人Host：陈秀卿 教授

报告摘要 Abstract:

In this talk, we focuses on a class of cancer invasion models that incorporate ECM remodeling and nonlinear diffusion. For this model, the introduction of nonlinear diffusion disrupts the well-coupled structure between the diffusion term and the haptotactic term, leading to the ineffectiveness of the effective methods utilized in linear diffusion model, thus posing a significant challenge. To address this, we have constructed a new functional that can alleviate the inherent difficulties caused by the low regularity of the haptotactic term. Using this approach, we are able to capture part of the long-time asymptotic behavior of the solution, ultimately verifying the uniform boundedness of the weak solution. Furthermore, by enhancing the convergence of cancer cells $u$ from $L^p$-norm to $L^\infty$-norm, we prove that, for some slow diffusion cases, the weak solution will eventually exhibit H\”older continuity.

报告人简介：

金春花，华南师范大学教授。长期从事非线性扩散模型相关理论的研究，研究工作发表在Bull. London Math. Soc.，J Nonlinear Sci.，Stud Appl Math.，Physica D， Nonlinearity，JDE，JDDE 等期刊。入选教育部新世纪优秀人才支持计划，主持包括国家自然科学基金面上项目，广东省杰出青年基金等在内的多项研究课题。