Global existence and blow-up for semilinear damped wave equations in three space dimensions

2018/07/11 by Masakazu Kato, Kato, Masakazu, Miku Sakuraba +1
Engineering · Mathematics · Physics and Astronomy · #35A01 #35E15 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1807.04327

openalex publication_date 2018/07/11 · openalex created_date 2018/07/19 · openalex updated_date 2026/07/28

Abstract

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the solutions. This paper is devoted to a proof of the Takamura's conjecture on the lifespan of solutions.

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