| LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = u^k（δu）^α |
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| 作者姓名： | FANG Daoyuan WANG Chengbo |
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| 摘 要： | This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in H^s and H^s for semilinear wave equations with polynomial nonlinearity in u and δu. This ill-posed result concerns the focusing type equations with nonlinearity on u and δtu.
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| 关 键 词： | 半线性波动函数 低正则性 非线性多项式 柯西问题 数学物理方程 |
| 收稿时间： | 3/4/2015 12:00:00 AM |
| 修稿时间： | 2014/10/4 0:00:00 |
LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE $\Box u=u^k(\partial u)^\alpha$ |
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| 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,Series B,2005,26(3):361-378. |
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| Authors: | FANG Daoyuan and WANG Chengbo |
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| Affiliation: | DepartmentofMathematics,ZhejiangUniversity,Hangzhou310027,China |
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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 $\partial_t u$. |
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| Keywords: | Semilinear wave equation Low regularity Local well-posedness Ill-posedness |
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