On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation - Couverture souple

Collot, Charles; Raphael, Pierre; Szeftel, Jeremie

Couverture souple

ISBN 10 : 1470436264 ISBN 13 : 9781470436261

Editeur : American Mathematical Society, 2019

Synopsis

The authors consider the energy super critical semilinear heat equation $\partial _{t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$ The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

A propos du livre

À propos de l'auteur

Charles Collot, Universite de Nice-Sophia Antipolis, France.

Pierre Raphael, Universite de Nice-Sophia Antipolis, France.

Jeremie Szeftel, Universite Paris 6, France.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 1470436264
• ISBN 13: 9781470436261
• Reliure: Broché
• Nombre de pages: 93
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible