Global existence of Landau–Lifshitz–Gilbert equation and self-similar blowup of Harmonic map heat flow on S2

Penghong Zhong, Ganshan Yang and Xuan Ma

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 174, issue C, 1-18

Abstract: Under the plane wave setting, the existence of small Cauchy data global solution (or local solution) of Landau–Lifshitz–Gilbert equation is proved. Some variable separation type solutions (include some small data global solution) and self-similar type solutions are constructed for the Harmonic map heat flow on S2. As far as we know, there is not any literature that presents the exact blowup solution of this equation. Some explicit solutions which include some finite time gradient-blowup solutions are provided. These blowup examples indicate a finite time blowup will happen in any spacial dimension.

Keywords: Landau–Lifshitz–Gilbert equation; Harmonic map heat flow; Self-similar; Blowup solution (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475420300410
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:174:y:2020:i:c:p:1-18

DOI: 10.1016/j.matcom.2020.02.002

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().