Smooth solution of the generalized system of ferro-magnetic chain

Boling Guo; Haiyang Huang

doi:10.3934/dcds.1999.5.729

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1999, Volume 5, Issue 4: 729-740. Doi: 10.3934/dcds.1999.5.729

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Smooth solution of the generalized system of ferro-magnetic chain

Boling Guo^1, and
Haiyang Huang^2,

1.
Institute of Applied Physics & Computational Math., Beijing 100088
2.
Dept. of Math., Beijing Normal University, Beijing, 100875

Received: July 31, 1998

Revised: March 31, 1999

Published: September 1999

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Abstract

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.

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Mathematics Subject Classification: 35D10, 35Q80.

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