知识与财富的链接
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．
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.
