"Layered solutions for a nonlocal Ginzburg-Landau model with periodic m" by Ko Shin Chen, Cyrill Muratov et al.
 

Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation

Document Type

Article

Publication Date

1-1-2023

Abstract

We study layered solutions in a one-dimensional version of the scalar Ginzburg-Landau equation that involves a mixture of a second spatial derivative and a fractional half-derivative, together with a periodically modulated nonlinearity. This equation appears as the Euler-Lagrange equation of a suitably renormalized fractional Ginzburg-Landau energy with a double-well potential that is multiplied by a 1-periodically varying nonnegative factor g(x) with (Formula presented). A priori this energy is not bounded below due to the presence of a nonlocal term in the energy. Nevertheless, through a careful analysis of a minimizing sequence we prove existence of global energy minimizers that connect the two wells at infinity. These minimizers are shown to be the classical solutions of the associated nonlocal Ginzburg-Landau type equation.

Identifier

85164987011 (Scopus)

Publication Title

Mathematics in Engineering

External Full Text Location

https://doi.org/10.3934/mine.2023090

e-ISSN

26403501

Issue

5

Volume

5

Grant

947054

Fund Ref

National Science Foundation

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