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| Blow up for Initial-Boundary Value Problem of WaveEquation with a Nonlinear Memory in 1-D |
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Citation： |
Ning-An LAI,Jianli LIU,Jinglei ZHAO.Blow up for Initial-Boundary Value Problem of WaveEquation with a Nonlinear Memory in 1-D[J].Chinese Annals of Mathematics B,2017,38(3):827~838 |
| Page view： 4339
Net amount： 2485 |
Authors： |
Ning-An LAI; Jianli LIU;Jinglei ZHAO |
Foundation： |
This work was supported by the National Natural Sicence
Foundation of China (Nos.11301489, 11401367,11501273), the
Natural Science Foundation of Zhejiang Province (Nos.LQ13A010013,
LY14A010010), and the Doctoral Fund of Ministry of Education of
China (No.20133108120002). |
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| Abstract： |
The present paper is devoted to studying the initial-boundary value
problem of a 1-D wave equation with a nonlinear memory:
$$u_{tt}-u_{xx}=\frac{1}{\Gamma(1-\gamma)}\int_0^t(t-s)^{-\gamma}|u(s)|^p\rmd
s.$$ The blow up result will be established when $p>1$ and
$0<\gamma<1$, no matter how small the initial data are, by
introducing two test functions and a new functional. |
Keywords： |
Blow up, Wave equation, Nonlinear memory, Initial-boundary value
problem |
Classification： |
35L05, 35L70 |
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