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VOL. 67 | 2015 Dynamics of topological defects in nonlinear field theories
Robert L. Jerrard

Editor(s) Luigi Ambrosio, Yoshikazu Giga, Piotr Rybka, Yoshihiro Tonegawa

Abstract

We survey recent results that characterize the dynamics, in a certain asymptotic limit, of interfaces in certain semilinear hyperbolic equations, as well as vortex filaments in semilinear hyperbolic systems. This survey includes a lengthy discussion of heuristic considerations, together with some complete proofs in simple model cases. We also present some novel recent approaches to problem that geometric evolution problem of timelike extremal submanifolds of Minkowski space, which governs the asymptotic dynamics of interfaces and vortex filaments.

Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1375.35276
MathSciNet: MR3587451

Digital Object Identifier: 10.2969/aspm/06710157

Subjects:
Primary: 35L71
Secondary: 35B40

Rights: Copyright © 2015 Mathematical Society of Japan

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