为了交流近年来在几何与非线性偏微分方程领域所取得的最新研究成果，讨论相关的前沿课题，同时促进相关领域的专家学者间的合作交流，丽水学院数学系和非线性分析研究所定于
报告题目：Test function method for blow-up phenomena of semilinear wave equations and their weakly coupled systems
报告者：Masahiro Ikeda (RIKEN and
报告摘要：In this talk we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems. We propose a framework of test function method and give a simple proof of the derivation of sharp upper bound of lifespan of solutions to nonlinear wave equations and their systems. We point out that for respective critical case, we use a family of self-similar solution to the standard wave equation including Gauss’s hypergeometric functions which are originally introduced by Zhou (1992). However, our framework is much simpler than that. As a consequence, we found new $(p,q)$-curve for the system $\partial_t^2u-\Delta u=|v|^q$, $\partial_t^2v-\Delta v=|u|^p$ and lifespan estimate for small solutions for new region.
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报告题目：Global well-posedness for the wave equation with a time-dependent scale invariant damping and a cubic convolution
报告者：Tomoyuki Tanaka (RIKEN AIP center/Nagoya University/Keio University/
报告摘要：In this talk, we consider global well-posedness for the wave equation with a time-dependent scale invariant damping, i.e., $\frac{2}{1+t}\dt u$ and a cubic convolution $(|x|^{-\ga}*u^2)u$, where $0<\ga<n$. For a power type nonlinearity, the work of D’Abbicco, Lucente and Reissig shows that a critical exponent, which divides global existence and blow-up for small solutions, is shifted because of the presence of the damping term. Our aim of this work is to determine two types of critical exponents of the problem with the cubic convolution. The one is for compactly supported initial data. The second is a critical exponent about the spatial decay condition on the data. This talk is based on a joint work with Masahiro Ikeda (RIKEN/Keio) and Kyouhei Wakasa (
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