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

Ning-An Lai; Yi Zhou

doi:10.3934/cpaa.2018072

Article Contents

2018, Volume 17, Issue 4: 1499-1510. Doi: 10.3934/cpaa.2018072

This issue Previous Article Global existence for systems of nonlinear wave and klein-gordon equations with compactly supported initial data Next Article Dynamical behavior for the solutions of the Navier-Stokes equation

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

Ning-An Lai^1,2, , and
Yi Zhou^2,

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
* Corresponding author: Ning-An Lai

Received: August 31, 2016

Revised: April 30, 2017

Published: April 2018

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.

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Abstract

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.

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Mathematics Subject Classification: 35L05, 35L70.

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References

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