报告时间：2020年8月15日（周六）15:00 -- 16:00

报告地点：主楼203室

报告题目：Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion

报告摘要: We shall report our recent progress on a principal eigenvalue problem of a linear second order elliptic operator with small/large diffusion. More specifically, we are concerned with the following eigenvalue problem: -D∆φ -2α∇m(x)∇φ + V (x)φ = λφ in Ω, complemented by a general boundary condition including Dirichlet boundary condition and Robin boundary condition: ∂φ/∂n + β(x)φ = 0 on ∂Ω, where β ∈ C(∂Ω) allows to be positive, sign-changing or negative, and n(x) is the unit exterior normal to ∂Ω at x. The domain Ω⊂ R^N  is bounded and smooth, the constants D > 0 and α > 0 are, respectively, the diffusive and advection coefficients, and m ∈ C^2(Ω) , V ∈ C(Ω) are given functions. We aim to determine the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient D → 0 or D → ∞. Our results, together with those by others where the Nuemann boundary case (i.e., β = 0 on ∂Ω) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. The talk is based on a joint work with Guanghui Zhang and Maolin Zhou.

报告人简介：彭锐，教授，博士生导师，江苏省特聘教授，入选“教育部新世纪优秀人才支持计划”， 获得“江苏省杰出青年基金”和“江苏省数学成就奖”，入选江苏省“333人才工程”中青年学科带头人。本科毕业于三峡大学，硕士毕业于东南大学，博士毕业于东南大学和澳大利亚新英格兰大学，曾在加拿大纽芬兰大学(AARMS资助)和美国明尼苏达大学IMA（美国NSF资助）从事博士后工作,  德国“洪堡学者”获得者。彭锐教授目前的主要研究兴趣包括偏微分方程、动力系统理论以及在生物学、传染病学和化学反应等领域的应用。已在Transactions of the American Mathematical Society、Journal of Functional Analysis、SIAM Journal on Mathematical Analysis、Indiana University Mathematics Journal、Journal of Nonlinear Science、Calculus of Variations and Partial Differential Equations、SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Physica D、Nonlinearity、European Journal of Applied Mathematics、Journal of Differential Equations等数学杂志发表学术论文多篇。