(In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation. (9th August 2013)

• Record Type: Journal Article
• Authors: VAN DEN BERG, JAN BOUWE; WILLIAMS, J. F.
• Is Part Of: European journal of applied mathematics. Volume 24:Number 6(2013:Dec.)
• Page Start: 921
• Page End: 948
• Publication Date: 2013-08-09
• Subjects: Landau–Lifshitz–Gilbert, -- Harmonic map heatflow, -- Schrödinger map flow, -- Asymptotic analysis, -- Blowup, -- Numerical simulations, -- Adaptive numerical methods; Mathematics -- Periodicals; 519
• DOI: 10.1017/S0956792513000247
• Languages: English
• ISSNs: 0956-7925

Abstract

Abstract : In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau–Lifshitz–Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic.