报告题目：Asymptotic stability of spiky steady states for the chemotaxis model of consumption type

报告人：李敬宇（东北师范大学，教授）

报告时间：2022年9月15日 15：30-16：30

报告地点：腾讯会议ID：233-795-119

校内联系人：李天然

报告摘要：We study the nonlinear stability of spiky solutions to a chemotaxis model of consumption type with singular signal-suppressed motility in the half space. We show that, when the physical no-flux boundary condition for the bacteria density and the nonhomogeneous Dirichlet boundary condition for the nutrient are prescribed, this chemotaxis model admits a unique smooth spiky steady state, and it is nonlinearly stable under appropriate perturbations. The challenge of the problem is that there are two types of singularities involved in the model: one is the logarithmic singularity of the sensitive function; and the other is the inverse square singularity of the motility. We employ a Cole-Hopf transformation to relegate the former singularity to a nonlocality that can be resolved by the method of anti-derivative. To deal with the latter singularity, we construct an approximate system that retains a key structure of the original singular system to establish the local-wellposedness, and develop a new strategy, which combines a weighted elliptic estimate and the weighted energy estimate, to close a priori estimate in the global theory.