Invited by Prof. Chunyou Sun of School of Mathematics and Statistics, Ph.D. Xinyu Mei fromShenzhen University will give a lecture.

Reporter:Muzheng Zhu

Title：OnTime-dependentasymptotic behaviorofsolutions for hyperbolic equations with time-dependent memory kernels

Time：10:00 a.m.,Dec. 10th, 2021

Location: Room 518, Polytechnic building

Abstract：In this talk, wegive a detailed study of long-time dynamics generatedby the wave equation with time-dependent speed of propagation and time-dependent memory kernel. Within the novel theory of process on time-dependent spaces and the correct mathematical setting of memory kernel, we firstestablish the global well-posedness result in extended time-dependent memoryspace. Under the exponential decay control, we develop furthersome new time-space (energy) estimates to overcome the mixed difficulties fromtime-dependent speed of propagation and memory kernel, then obtain the dissipativity and regularity of the dynamicalprocess. In this work, we further study the existence and regularity of the time-dependent global attractor.