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| LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE $\Box u=u^k(\partial u)^\alpha$ |
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Citation： |
FANG Daoyuan,WANG Chengbo.LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE $\Box u=u^k(\partial u)^\alpha$[J].Chinese Annals of Mathematics B,2005,26(3):361~378 |
| Page view： 1309
Net amount： 1345 |
Authors： |
FANG Daoyuan; WANG Chengbo |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271108). |
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| Abstract： |
This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in $H^s$ and $\dot{H}^s$ for semilinear wave equations with polynomial nonlinearity in $u$ and $\partial u$. This ill-posed result concerns the focusing type equations with nonlinearity on $u$ and $\partial_t u$. |
Keywords： |
Semilinear wave equation, Low regularity, Local well-posedness, Ill-posedness |
Classification： |
35L15, 35L70 |
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