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

Nicholas D. Alikakos; Giorgio Fusco

Journal of the European Mathematical Society (2015)

  • Volume: 017, Issue: 7, page 1547-1567
  • ISSN: 1435-9855

Abstract

top
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.

How to cite

top

Alikakos, Nicholas D., and Fusco, Giorgio. "A maximum principle for systems with variational structure and an application to standing waves." Journal of the European Mathematical Society 017.7 (2015): 1547-1567. <http://eudml.org/doc/277679>.

@article{Alikakos2015,
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.},
author = {Alikakos, Nicholas D., Fusco, Giorgio},
journal = {Journal of the European Mathematical Society},
keywords = {vector Allen–Cahn equation; standing waves; periodic domains; maximum principle for (vector) minimizers; vector Allen-Cahn equation; standing waves; periodic domains; maximum principle for (vector) minimizers},
language = {eng},
number = {7},
pages = {1547-1567},
publisher = {European Mathematical Society Publishing House},
title = {A maximum principle for systems with variational structure and an application to standing waves},
url = {http://eudml.org/doc/277679},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Alikakos, Nicholas D.
AU - Fusco, Giorgio
TI - A maximum principle for systems with variational structure and an application to standing waves
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 7
SP - 1547
EP - 1567
AB - 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.
LA - eng
KW - vector Allen–Cahn equation; standing waves; periodic domains; maximum principle for (vector) minimizers; vector Allen-Cahn equation; standing waves; periodic domains; maximum principle for (vector) minimizers
UR - http://eudml.org/doc/277679
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.