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| Global Existence and Blow-up for Semilinear Wave Equations with Variable Coefficients |
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Citation： |
Qian LEI,Han YANG.Global Existence and Blow-up for Semilinear Wave Equations with Variable Coefficients[J].Chinese Annals of Mathematics B,2018,39(4):643~664 |
| Page view： 680
Net amount： 837 |
Authors： |
Qian LEI; Han YANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11501395, 71572156). |
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| Abstract： |
The authors consider the critical exponent problem for the variable
coefficients wave equation with a space dependent potential and
source term. For sufficiently small data with compact support, if
the power of nonlinearity is larger than the expected exponent, it
is proved that there exists a global solution. Furthermore, the
precise decay estimates for the energy, $L^2$ and $L^{p+1}$ norms of
solutions are also established. In addition, the blow-up of the
solutions is proved for arbitrary initial data with compact support
when the power of nonlinearity is less than some constant. |
Keywords： |
Semilinear wave equations, Global existence, Energy decay, $L^2$ and $L^{p+1}$ estimates, Blow up |
Classification： |
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