Non-existence of weak solutions to nonlinear damped wave equations in exterior domains

✍ Scribed by Takayoshi Ogawa; Hiroshi Takeda

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 395 KB
• Volume: 70
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.07.025

✦ Synopsis

We consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain Ω,

support, we prove the non-existence of non-negative global solutions of the above problem.

We employ the Kaplan-Fujita [H. Fujita, On the blowing up of solutions of the Cauchy problem for u t = ∆u + u 1+α , J. Sci. Univ. Tokyo. Sec. I. 13 (1966) 109-124; S. Kaplan, On the growth of solutions quasi-linear parabolic equations, Comm. Pure Appl. Math. 16 (1963) 305-330] method to avoid the difficulty of the reflection from the boundary.