Non-existence of weak solutions to nonlinear damped wave equations in exterior domains
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- 作者：Takayoshi Ogawa ; Hiroshi Takeda
- 关键词：Nonlinear damped wave equations ; Critical exponent ; Exterior domains ; Finite time blow-up
- 刊名：Nonlinear Analysis
- 出版年：2009
- 出版时间：15 May 2009
- 年：2009
- 卷：70
- 期：10
- 页码：3696-3701
- 全文大小：394 K
文摘
We consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain Ω, When and the initial data having compact 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 ut=Δu+u1+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.