主讲人：张晓燕 山东大学教授
时间：2026年5月15日16：00
地点：徐汇校区三号楼332室
举办单位：必威西汉姆联
主讲人介绍：张晓燕，山东大学数学公司教授、博士生导师，从事非线性泛函分析的理论及其应用、偏微分方程和生物数学模型等方向的研究，近年来在非线性算子理论、浮游植物生长模型、扩散捕食-被捕食模型、分数阶p-Laplacian微分方程及反应扩散系统等领域取得一系列成果，已在国内外重要期刊发表论文40余篇。主持国家自然科学基金项目3项和山东省自然科学基金项目2项等。
内容介绍：We study a monostable reaction-diffusion-advection free boundary problem with a preferred density boundary condition, which models the spatial spread of a species. The species tends to maintain a specific density $\delta＞0$ at the spreading fronts, and this condition significantly affects the invasion dynamics. We establish the well-posedness of the solution and rigorously prove a trichotomy for population evolution: spreading occurs when $0＜\delta＜1$, transition occurs when $\delta=1$, and vanishing happens when $\delta＞1$. In the spreading case, we precisely obtain for the first time the asymptotic speeds of the left and right spreading fronts and their dependence on the advection strength $\beta$. Moreover, we reveal a structural transition in the left propagation pattern from a semi-wave to a traveling wave when $\beta$ exceeds a threshold $\beta^*$. This study systematically elucidates the coupling influence of the preferred density and advection effects on biological invasion dynamics.