偏微分方程式セミナー: Global existence and lifespan for semilinear wave equations with mixed nonlinear terms, Wei Dai 氏

開催日時

2019年5月24日 16時30分 ～ 2019年5月24日 18時00分

場所

北海道大学理学部3号館3-309室

講演者

Wei Dai 氏 (北海道大学)

Firstly, we study the equation \(\square u = |u|^{q_c}+ |\partial u|^p\) with small data, where \(q_c\) is the critical power of Strauss conjecture and \(p\geq q_c\). We obtain the optimal estimate of the lifespan \(\ln ({T_\varepsilon})\approx\varepsilon^{-q_c(q_c-1)}\) in \(n=3\), and improve the lower bound of \(T_\varepsilon\) from \(\exp ({c\varepsilon^{-(q_c-1)}})\) to \(\exp ({c\varepsilon^{-(q_c-1)^2/2}})\) in \(n=2\). Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations \(\square u = |v|^q\), \(\square v = |\partial_t u|^p\) in 3-dimensional space with \(q<2\). We obtain that this system admits a global solution above a \(p-q\) curve for spherically symmetric data. On the contrary, we get a new region where the solution will blow up.

世話人：黒田 紘敏、浜向 直