# American Institute of Mathematical Sciences

July  2018, 17(4): 1499-1510. doi: 10.3934/cpaa.2018072

## Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions

 1 Institute of Nonlinear Analysis and Department of Mathematics, Lishui University, Lishui 323000, China 2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China

* Corresponding author: Ning-An Lai

Received  September 2016 Revised  May 2017 Published  April 2018

Fund Project: The first author is partially supported by Zhejiang Province Science Foundation(LY18A010008), NSFC(11501273, 11726612, 11771359, 11771194), Chinese Postdoctoral Science Foundation(2017M620128), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B)(201601). The second author is supported by Key Laboratory of Mathematics for Nonlinear Sciences(Fudan University), Ministry of Education of China, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, NSFC (11726611, 11421061), 973 program (2013CB834100) and 111 project

This paper focuses on the initial boundary value problem of semilinear wave equation in exterior domain in two space dimensions with critical power. Based on the contradiction argument, we prove that the solution will blow up in a finite time. This complements the existence result of supercritical case by Smith, Sogge and Wang [20] and blow up result of subcritical case by Li and Wang [14] in two space dimensions.

Citation: Ning-An Lai, Yi Zhou. Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1499-1510. doi: 10.3934/cpaa.2018072
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