报告题目：Qualitative properties for a strongly damped semilinear wave equation with time-varying source and singular dissipation

报告人：中国海洋大学方钟波教授

报告时间：2024年03月29日9:30-10:30

报告地点：数统院137

报告摘要：We study theglobal well-posedness and blow-up phenomena for a strongly damped semilinear wave equation with time-varying source and singular dissipative terms under the null Dirichlet boundary condition. Based on cut-off technique, multiplier method, contraction mapping principle, and the modified potential well method, we establish the local well-posedness and obtain the threshold between the existence and nonexistence of the global solution (including the critical case). Meanwhile, with the aid of modified differential inequality technique, the blow-up result of the solutions with arbitrarily positive initial energy and the lifespan of the blow-up solutions are derived.

报告人简介：方钟波，中国海洋大学数学科学学院教授，研究方向是非线性偏微分方程及其应用。在《Calc. Var. Partial Differential Equations》、《Z. Angew. Math. Phys.》、《Nonlinear Anal-Real.》、《Math. Nachr.》、《Adv. Nonlinear Anal.》等上发表学术论文100余篇。主持或参与省部级以上科研和教研项目20多项，获得“第六届青岛市高校教学名师”、“第五届山东省优秀研究生指导教师”、“山东省优秀硕士学位论文指导教师”、“山东省优秀学士学位论文指导教师”、“山东省研究生优秀科研成果奖指导教师”、“山东省高等学校优秀科研成果奖(首位)”、“山东省优秀教学成果二等奖(首位)”等20多项荣誉。