活动时间：2022-09-28 17:00

活动地点：腾讯会议 543-948-743

主讲人：M. Reissig

主讲人中文简介：

德国佛莱贝格科技大学（TU Bergakademie Freiberg, Germany），教授，博士生导师，主要研究偏微分方程解的适定性及应用分析。中德“偏微分方程分析及应用”国际合作项目德方重要成员，先后组织21个国际数学学术会议及分组会议，50余次受邀在国际数学学术会议上作学术报告，任若干个国际数学期刊的编委，在包括数学四大顶级期刊《Math. Anal.》在内的国际重要核心期刊上发表高水平论文100余篇，主持德国国家、州政府基金20余项，出版学术专著5部，培养了10余名优秀的博士生，在英国、德国、法国等的大学里任副教授、教授。

活动内容摘要：

In this lecture we discuss the Cauchy problem for semilinear de Sitter models from cosmology. These are wave models with integrable time-dependent speed of propagation and friction and mass term with constant coefficients. The nonlinearity on the right-hand side is supposed to be of power type. The main question is that for a critical exponent a threshold between global (in time) small data Sobolev solutions and blow-up phenomena even for small data. We discuss only the global (in time) existence part. We explain the treatment of the linear part and the treatment of the nonlinear part appearing in a fixed point formulation for Sobolev solutions. Here different tools from Harmonic Analysis are used. We explain for different regularity of data the admissible set of exponents in power nonlinearities. The question for critical exponent remains open.

主持人：秦玉明