Finite time blow-up for a kind of initial-boundary value problem of semilinear damped wave equation

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• 作者：Ningan Lai and Silu Yin
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：40
• 期：4
• 页码：1223-1230
• 全文大小：164K
• ISSN：1099-1476

文摘

In this paper, we consider the initial-boundary value problem of semilinear damped wave equation u_tt−Δu + u_t=|u|^p with power equation-construct="true" class="math-equation-construct">equation-image="true" class="math-equation-image">equation-mathml="true" class="math-equation-mathml" style="display:none">p=1+2n in an exterior domain. Blow-up result in a finite time will be established in higher dimensions (n≥3), no matter how small the initial data are. A special test function will be constructed, and then, we obtain the blow-up result by a contradiction argument. Copyright