Séminaire ACSIOM :

Le 10 mars 2009 à 10:00 - salle 431

Présentée par Nara Mitsunori - Tokyo Inst. of Technology

Stability of planar waves in the Allen-Cahn equation

We consider the Cauchy problem of the Allen-Cahn equation on R^n. Our main interest is to analyze the large time behavior of solutions and asymptotic stability of the planar waves. Suitable supersolutions and subsolutions are constructed and some notions from dynamical systems theory are introduced.