Existence of Traveling Wave Solutions for Density-Dependent Diffusion Competitive Systems
科研大讨论系列报告
报告题目(Title)： Existence of Traveling Wave Solutions for Density-Dependent Diffusion Competitive Systems
报告人(Speaker)：王飏 副教授 （山西大学）
地点(Place)：腾讯会议ID：233319487 密码:508826
时间(Time)：2024 年 11月 1日 下午3:00-4:00
邀请人(Inviter)：黎雄
报告摘要
In this talk, we focus on the existence of traveling wave solutions for two-species competitive systems with density-dependent diffusion. Density-dependent diffusion is a form of nonlinear diffusion that degenerates at the origin, rendering traditional methods for proving the existence of traveling wave solutions for competitive systems with linear diffusion inapplicable. To address this diffusion degeneracy, we construct a nonlinear invariant region, denoted as Ω, near the origin. Utilizing the method of phase plane analysis, we demonstrate the existence of traveling wave solutions that connect the origin to the unique coexistence state when the wave speed c exceeds a certain positive threshold c*. Furthermore, when one species exhibits density-dependent diffusion and the other exhibits linear diffusion, we employ a change of variables and the central manifold theorem to establish the existence of a minimal wave speed c≥c*. For wave speeds c≥c*, traveling wave solutions that connect the origin to the unique coexistence state persist. Notably, at c=c*, we observe that one component of the traveling wave solution is of a sharp type, while the other is smooth. This phenomenon is distinct from what is observed in systems with linear diffusion or scalar equations. This is a joint work with Xuanyu Lv, Fan Liu and Xiaoguang Zhang.
主讲人简介
王飏，山西大学数学科学学院副教授，硕士生导师。主要研究方向为扩散系统的传播问题。先后主持国家自然科学基金1项、省部级项目4项。在《Nonlinearity》《Proc. Roy. Soc. Edinburgh Sect. A》《J. Math. Phys》《Z. Angew. Math. Phys》等杂志上发表论文10余篇。指导2名硕士研究生获山西省优秀学位论文。
