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May  2019, 18(3): 1351-1358. doi: 10.3934/cpaa.2019065

Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up

 1 College of Science, Harbin Engineering University, 150001, China 2 College of Computer Science and Technology, Harbin Engineering University, 150001, China 3 Department of Mathematics, University of Texas, Arlington, TX 76019, USA

* Corresponding author

Received  June 2018 Revised  September 2018 Published  November 2018

Fund Project: The first author was supported by the National Natural Science Foundation of China (11801114), the Heilongjiang Postdoctoral Foundation (LBH-Z15036), the China Scholarship Council (201706685064), the Fundamental Research Funds for the Central Universities. The second author was supported by the National Natural Science Foundation of China (11871017), the China Postdoctoral Science Foundation (2013M540270), the Fundamental Research Funds for the Central Universities.

By introducing a new increasing auxiliary function and employing the adapted concavity method, this paper presents a finite time blow up result of the solution for the initial boundary value problem of a class of nonlinear wave equations with both strongly and weakly damped terms at supercritical initial energy level.

Citation: Yanbing Yang, Runzhang Xu. Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up. Communications on Pure &amp; Applied Analysis, 2019, 18 (3) : 1351-1358. doi: 10.3934/cpaa.2019065
References:

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References:
Obtained results and open problems for problem (1)-(3)
 Global existence Asymptotic behavior Blow up Subcritical initial energy $E(0)d$ Open problem Open problem $\omega=0$, $\mu>0$$\omega=0, \mu=0Reference [4] \omega>0, \mu>0 \omega>0, \mu=0 \omega=0, \mu>0$$\omega=0$, $\mu=0$Present paper
 Global existence Asymptotic behavior Blow up Subcritical initial energy $E(0)d$ Open problem Open problem $\omega=0$, $\mu>0$$\omega=0, \mu=0Reference [4] \omega>0, \mu>0 \omega>0, \mu=0 \omega=0, \mu>0$$\omega=0$, $\mu=0$Present paper
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