October  1999, 5(4): 729-740. doi: 10.3934/dcds.1999.5.729

Smooth solution of the generalized system of ferro-magnetic chain

1. 

Institute of Applied Physics & Computational Math., Beijing 100088, China

2. 

Dept. of Math., Beijing Normal University, Beijing, 100875, China

Received  August 1998 Revised  April 1999 Published  July 1999

In this paper, we consider the initial value problem with periodic boundary condition for a class of general systems of the ferromagnetic chain

$z_t=-\alpha z\times (z\times z_{x x})+ z\times z_{x x}+z\times f(z), \qquad (\alpha \geq 0).$

The existence of unique smooth solutions is proved by using the technique of spatial difference and a priori estimates of higher-order derivatives in Sobolev spaces.

Citation: Boling Guo, Haiyang Huang. Smooth solution of the generalized system of ferro-magnetic chain. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 729-740. doi: 10.3934/dcds.1999.5.729
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