Taiwanese Journal of Mathematics

Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrödinger Type

Yutian Lei

Advance publication

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Abstract

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.

Article information

Source
Taiwanese J. Math., Advance publication (2020), 20 pages.

Dates
First available in Project Euclid: 17 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1584432073

Digital Object Identifier
doi:10.11650/tjm/200302

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35K51: Initial-boundary value problems for second-order parabolic systems 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

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

Citation

Lei, Yutian. Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrödinger Type. Taiwanese J. Math., advance publication, 17 March 2020. doi:10.11650/tjm/200302. https://projecteuclid.org/euclid.twjm/1584432073


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