Pseudodifferential multi-product representation of the solution operator of a parabolic equation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Comm. Partial Differential Equations Année : 2009

Pseudodifferential multi-product representation of the solution operator of a parabolic equation

Résumé

By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality.
Fichier principal
Vignette du fichier
parabolic-multiproduct.pdf (266.16 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00216207 , version 1 (24-01-2008)
hal-00216207 , version 2 (17-04-2009)

Identifiants

Citer

Hiroshi Isozaki, Jérôme Le Rousseau. Pseudodifferential multi-product representation of the solution operator of a parabolic equation. Comm. Partial Differential Equations, 2009, 34 (7), pp.625 - 655. ⟨10.1080/03605300903017330⟩. ⟨hal-00216207v2⟩
192 Consultations
132 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More