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October, 2020 Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrödinger Type
Yutian Lei
Taiwanese J. Math. 24(5): 1229-1248 (October, 2020). DOI: 10.11650/tjm/200302


This paper is concerned with the asymptotic behavior of the classical solutions of a Landau-Lifshitz-Schrödinger-type problem with initial-boundary values when the parameter $\varepsilon$ goes to zero. We establish several uniform estimates of $u_{\varepsilon}$ by a conservation result and the standard parabolic method. Based on these results, we obtain parabolic behavior in the dissipative case and non-parabolic behavior of the semi-classical limits of those solutions respectively.


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Yutian Lei. "Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrödinger Type." Taiwanese J. Math. 24 (5) 1229 - 1248, October, 2020.


Received: 29 October 2019; Revised: 17 February 2020; Accepted: 13 March 2020; Published: October, 2020
First available in Project Euclid: 17 March 2020

MathSciNet: MR4152664
Digital Object Identifier: 10.11650/tjm/200302

Primary: 35B40 , 35K51 , 35Q55

Keywords: heat flow of harmonic map , Landau-Lifshitz-Schrödinger equation , uniform estimate

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 5 • October, 2020
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