Blow up for initial-boundary value problem of wave equation with a nonlinear memory in 1-D
Blow up for initial-boundary value problem of wave equation with a nonlinear memory in 1-D
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一维非线性记忆波动方程初边值问题的爆炸
DOI：
10.1007/s11401-017-1098-1
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发表时间：
2017-05
期刊：
影响因子：
--
通讯作者：
Jinglei Zhao
中科院分区：
文献类型：
--
作者：
Ning-An Lai;Jianli Liu;Jinglei Zhao
AbstractThe present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: $${u_{tt}} - {u_{xx}} = \frac{1}{{\Gamma \left( {1 - \gamma } \right)}}\int_0^t {{{\left( {t - s} \right)}^{ - \gamma }}{{\left| {u\left( s \right)} \right|}^p}ds} .$$utt−uxx=1Γ(1−γ)∫0t(t−s)−γ|u(s)|pds.
The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.
AbstractThe present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: $${u_{tt}} - {u_{xx}} = \frac{1}{{\Gamma \left( {1 - \gamma } \right)}}\int_0^t {{{\left( {t - s} \right)}^{ - \gamma }}{{\left| {u\left( s \right)} \right|}^p}ds} .$$utt−uxx=1Γ(1−γ)∫0t(t−s)−γ|u(s)|pds.
The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.
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DOI：
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发表时间：
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影响因子：
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