【数学与统计及交叉学科前沿论坛------高端学术讲座第116场】

报告题目：Asymptotics for Solutions of the Porous Medium Equation on Manifolds with Conical Singularities

报告人：Elmar Schrohe, Ph.D., Professor, Institut für Analysis, Leibniz Universität Hannover

时间：2024年9月10日（周二）14:00—15:00

地点：阜成路校区综合楼1116会议室

报告摘要: We study the porous medium equation (PME) on a manifold with (possibly warped) conical singularities. It models e.g. the flow of gas in porous rock. Given an everywhere strictly positive initial datum in a suitable Mellin Sobolev space with asymptotics we establish the existence of a short time solution to the PME via maximal regularity techniques. It turns out that the possible asymptotics are determined by the eigenvalues of the Laplacian on the cross-section of the cone.

报告人简介: Professor Doctor Elmar Schrohe is the director of the Institute of Analysis at Leibniz University Hannover, and a principal investigator of the Graduate School 2491 "Fourier Analysis and Spectral Theory" in Göttingen. He significantly contributes to the field of partial differential equations and complex analysis, whose work has been published in numerous journals, and he is a respected reviewer for Mathematical Reviews. His academic leadership is not limited to his research and teaching. Professor Schrohe has also served as the Dean of the Faculty for Mathematics and Physics and as the Speaker of the Research Training Network "Analysis, Geometry, and String Theory" at Leibniz University Hannover. His service to the academic community extends to being a member of the Evaluation Committee for Dutch Universities and the EU network "Geometric Analysis."