A NONHOMOGENEOUS BOUNDARY-VALUE PROBLEM FOR THE MODIFIED ANISOTROPIC HEISENBERG SPIN CHAIN POSED ON A FINITE DOMAIN

Abstract

This article is concerned with the Modified Anisotropic Heisenberg Spin Chain. We prove that the associated nonhomogeneous initial-boundary value problem has a unique globally smooth solution in $H^{2k+1}(m, n)$ for $k\geq 1$. Our main new ingredient is a technique of spatial difference and crucial uniformed estimates of the step-size $h.$ Meanwhile, to prove the global existence, we overcome drawbacks which are not exist in corresponding Cauchy problem.