Lifespan estimate for classical damped wave equations with some initial data

Date
2024/01/19 Fri 16:00 - 17:00
Speaker
Kazumasa Fujiwara
Affiliation
Faculty of Advanced Science and Technology, Ryukoku University
Abstract

In this talk, we investigate the lifespan estimate for mild solutions to the classical damped wave equation with power-type nonlinearity without gauge invariance. Previous studies have delved into the nonexistence of solutions when the initial condition satisfies the following criterion: the Fourier 0 mode of the sum of the initial position and speed is 0. However, to the best of the authors' knowledge, the complete understanding of whether and how solutions undergo blowup at a finite time remains elusive when the initial data fails to meet the aforementioned condition. In this talk, we extend the blowup condition and show the corresponding lifespan estimate. This talk is based on joint works with Prof. Vladimir Georgiev at Pisa University.