偏微分方程式セミナー(2017/10/13): Blow-up of solutions to critical semilinear wave equations with variable coefficients

2017年 　 10月 13日 16時 30分 ～ 2017年 　 10月 13日 17時 30分

We consider the initial value problem for critical semilinear wave equations with variable coefficients arising in asymptotically flat space times. The perturbations of Laplace operator are assumed to be smooth and decay exponentially fast at infinity. For the usual Laplacian case, Yordanov and Zhang (2006) or Zhou (2007) showed the blow-up result in the critical case. Also, Takamura and Wakasa (2011) or Zhou and Han (2014) have obtained the sharp upper bound of the lifespan in the critical case. Our purpose in this talk is to give the blow-up result and sharp upper bound of the lifespan which has simpler proof than that of Zhou and Han. This is a joint work with Professor Borislav Yordanov.