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Extrapolation methods to solve non-autonomous retarded partial differential equations

Abdelaziz Rhandi — 1997

Studia Mathematica

Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.

The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure

Giorgio Metafune; Jan Prüss; Abdelaziz Rhandi; Roland Schnaubelt — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We show that the domain of the Ornstein-Uhlenbeck operator on $L^{p}$ $(ℝ^{N}, μ d x)$ equals the weighted Sobolev space $W^{2, p} (ℝ^{N}, μ d x)$ , where $μ d x$ is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.

Positivity and stability for a system of transport equations with unbounded boundary perturbations.

D'Apice, Ciro; El Habil, Brahim; Rhandi, Abdelaziz — 2009

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Currently displaying 1 – 3 of 3

Extrapolation methods to solve non-autonomous retarded partial differential equations

The domain of the Ornstein-Uhlenbeck operator on an L p -space with invariant measure

Positivity and stability for a system of transport equations with unbounded boundary perturbations.

The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure