JournalsjemsVol. 17, No. 7pp. 1547–1567

A maximum principle for systems with variational structure and an application to standing waves

  • Nicholas D. Alikakos

    University of Athens, Greece

  • Giorgio Fusco

    Università degli Studi dell'Aquila, Italy
A maximum principle for systems with variational structure and an application to standing waves cover
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Abstract

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.

Cite this article

Nicholas D. Alikakos, Giorgio Fusco, A maximum principle for systems with variational structure and an application to standing waves. J. Eur. Math. Soc. 17 (2015), no. 7, pp. 1547–1567

DOI 10.4171/JEMS/538