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

Yitong Pei; Shasha Bian; Boling Guo; Wuming Liu

doi:10.11948/20220302

2023 Volume 13 Issue 1

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Yitong Pei, Shasha Bian, Boling Guo, Wuming Liu. A NONHOMOGENEOUS BOUNDARY-VALUE PROBLEM FOR THE MODIFIED ANISOTROPIC HEISENBERG SPIN CHAIN POSED ON A FINITE DOMAIN[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 470-485. doi: 10.11948/20220302

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Yitong Pei, Shasha Bian, Boling Guo, Wuming Liu. A NONHOMOGENEOUS BOUNDARY-VALUE PROBLEM FOR THE MODIFIED ANISOTROPIC HEISENBERG SPIN CHAIN POSED ON A FINITE DOMAIN[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 470-485. doi: 10.11948/20220302

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

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
2.
Graduate School of China Academy of Engineering Physics, 100088, Beijing, China
3.
Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, 100088, Beijing, China

Corresponding author: Email: 1825166115@qq.com(S. Bian)

Abstract

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.
- The Modified Anisotropic Heisenberg Spin Chain /
- globally smooth solution /
- initial-boundary value problem /
- spatial difference method
MSC: 35Q55, 35L70, 35Q35, 76B15

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References

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