ASYMPTOTICALLY SELF-SIMILAR GLOBAL SOLUTIONS FOR HARDY-H ÉNON PARABOLIC SYSTEMS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Differential Equations and Applications Année : 2022

ASYMPTOTICALLY SELF-SIMILAR GLOBAL SOLUTIONS FOR HARDY-H ÉNON PARABOLIC SYSTEMS

Résumé

In this paper we study the nonlinear parabolic system @tu = u+a|x| |v| p 1 v, @tv = v + b|x| ⇢ |u| q 1 u, t > 0, x 2 R N \{0}, N 1, a, b 2 R, 0  < min(N, 2), 0 < ⇢ < min(N, 2), p, q > 1. Under conditions on the parameters p, q, and ⇢ we show the existence and uniqueness of global solutions for initial values small with respect of some norms. In particular, we show the existence of self-similar solutions with initial value = ('1, '2), where '1, '2 are homogeneous initial data. We also prove that some global solutions are asymptotic for large time to self-similar solutions.
Fichier principal
Vignette du fichier
NoDEA-S-17-00230.pdf (889.24 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03868436 , version 1 (23-11-2022)

Identifiants

Citer

Byrame Ben Slimene. ASYMPTOTICALLY SELF-SIMILAR GLOBAL SOLUTIONS FOR HARDY-H ÉNON PARABOLIC SYSTEMS. Differential Equations and Applications, 2022, 4, pp.439-462. ⟨10.7153/dea-2019-11-21⟩. ⟨hal-03868436⟩
15 Consultations
29 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More