Advanced Studies in Pure Mathematics

Dynamics of topological defects in nonlinear field theories

Robert L. Jerrard

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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.

Article information

Source
Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 157-224

Dates
Received: 26 March 2013
Revised: 4 July 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916037

Digital Object Identifier
doi:10.2969/aspm/06710157

Mathematical Reviews number (MathSciNet)
MR3587451

Zentralblatt MATH identifier
1375.35276

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Jerrard, Robert L. Dynamics of topological defects in nonlinear field theories. Variational Methods for Evolving Objects, 157--224, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710157. https://projecteuclid.org/euclid.aspm/1539916037


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