Blow-up of solutions to critical semilinear wave equations with variable coefficients |
| |
Authors: | Kyouhei Wakasa Borislav Yordanov |
| |
Affiliation: | 1. Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba, 278-8510, Japan;2. Office of International Affairs, Hokkaido University, Kita 15, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0815, Japan;3. Institute of Mathematics, Sofia, Bulgaria |
| |
Abstract: | We verify the critical case of Strauss' conjecture [30] concerning the blow-up of solutions to semilinear wave equations with variable coefficients in , where . The perturbations of Laplace operator are assumed to be smooth and decay exponentially fast at infinity. We also obtain a sharp lifespan upper bound for solutions with compactly supported data when . The unified approach to blow-up problems in all dimensions combines several classical ideas in order to generalize and simplify the method of Zhou [43] and Zhou & Han [45]: exponential “eigenfunctions” of the Laplacian [37] are used to construct the test function for linear wave equation with variable coefficients and John's method of iterations [13] is augmented with the “slicing method” of Agemi, Kurokawa and Takamura [1] for lower bounds in the critical case. |
| |
Keywords: | Corresponding author. |
本文献已被 ScienceDirect 等数据库收录! |
|