| 能量不等式和抛物单调不等式成立的一个充分条件 |
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| 引用本文： | 周春琴,周树清.能量不等式和抛物单调不等式成立的一个充分条件[J].上海交通大学学报,1999,33(6):661-665. |
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| 作者姓名： | 周春琴 周树清 |
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| 作者单位： | 上海交通大学,应用数学系,上海,200030 |
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| 基金项目： | 国家自然科学基金,国家教委博士点基金 |
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| 摘 要： | 讨论了含有底阶项铁磁链系统的Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ方程即非齐次调和映射流方程的Ｃａｕｃｈｙ问题．该问题弱解的能量不等式和抛物单调不等式在证明弱解的正则性时起关键作用．文中定义了该问题弱解满足的驻条件，给出了驻条件成立的充分条件，并且在驻条件下证明了弱解满足能量不等式和抛物单调不等式．
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| 关 键 词： | 能量不等式 抛物单调不等式 非齐次调和映射流方程 上Minkowski q－容量 驻条件 |
| 修稿时间： | 1997-06-01 |
Sufficient Condition of Energy Inequality and Parabolic Monotonicity Inequality |
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| ZHOU Chun-qin,ZHOU Shu-qing.Sufficient Condition of Energy Inequality and Parabolic Monotonicity Inequality[J].Journal of Shanghai Jiaotong University,1999,33(6):661-665. |
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| Authors: | ZHOU Chun-qin ZHOU Shu-qing |
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| Abstract: | Cauchy problem of Landau Lifshitz equation with low order terms for ferromagnetic spin system (i.e. the heat flow of inhomogeneous harmonic map equation) was discussed. The energy inequality and parabolic monotonicity inequality is essential for the regularity of a weak solution to this problem. Here a kind of stationary hypersis satisfied by a weak solutions to this problem was defined, and some sufficient conditions for stationary hypersis were given. Moreover, under the stationary hypersis these important inequalities were established. |
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| Keywords: | energy inequality parabolic monotonicity inequality harmonic map upper Minkowski q content stationary hypersis |
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