Existence and stability of discontinuous stationary solutions in a receptor-based model with hysteresis in higher-dimensional domains

主讲人：张聪晖 北京建筑大学讲师

时间：2024年12月9日9：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：张聪晖，讲师。中国人民大学博士，师从Izumi Takagi教授，博士期间曾赴日本东北大学进行为期16个月的联合培养，合作导师Goro Akagi教授；清华大学博士后，合作导师章梅荣教授，获得中国博士后科学基金，清华大学“水木学者”特别资助等。在《SIAM Journal on Mathematical Analysis》、《Journal of Differential Equations》、《Discrete and Continuous Dynamical Systems-A》等数学期刊发表论文十余篇。

内容介绍：We consider a receptor-based model which arises from the modeling of interactions between intracellular processes and diffusible signaling factors. By applying the variational method, we prove the existence of stationary solutions with jump discontinuity. Then a singular perturbation problem with discontinuous nonlinearity is studied based on the patching argument and the implicit function theorem, to obtain a solution with a single transition layer. Moreover, we derive a sufficient condition for the stability of stationary solutions with jump discontinuity. This talk is based on a joint work with Professors Akagi Goro and Izumi Takagi.