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A difference-differential analogue of the Burgers equations and some models of economic development
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 |
$z_t=-\alpha z\times (z\times z_{x x})+ z\times z_{x x}+z\times f(z), \qquad (\alpha \geq 0).$
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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