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The Super-Diffusive Singular Perturbation Problem

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Bibliographische Detailangaben
Titel:	The Super-Diffusive Singular Perturbation Problem
Autoren:	Edgardo Alvarez, Carlos Lizama
Quelle:	Mathematics, Vol 8, Iss 3, p 403 (2020)
Verlagsinformationen:	MDPI AG
Publikationsjahr:	2020
Bestand:	Directory of Open Access Journals: DOAJ Articles
Schlagwörter:	singular perturbation, fractional partial differential equations, analytic semigroup, super-diffusive processes, Mathematics, QA1-939
Beschreibung:	In this paper we study a class of singularly perturbed defined abstract Cauchy problems. We investigate the singular perturbation problem ( P ϵ ) ϵ α D t α u ϵ ( t ) + u ϵ ′ ( t ) = A u ϵ ( t ) , t ∈ [ 0 , T ] , 1 < α < 2 , ϵ > 0 , for the parabolic equation ( P ) u 0 ′ ( t ) = A u 0 ( t ) , t ∈ [ 0 , T ] , in a Banach space, as the singular parameter goes to zero. Under the assumption that A is the generator of a bounded analytic semigroup and under some regularity conditions we show that problem ( P ϵ ) has a unique solution u ϵ ( t ) for each small ϵ > 0 . Moreover u ϵ ( t ) converges to u 0 ( t ) as ϵ → 0 + , the unique solution of equation ( P ) .
Publikationsart:	article in journal/newspaper
Sprache:	English
Relation:	https://www.mdpi.com/2227-7390/8/3/403; https://doaj.org/toc/2227-7390; https://doaj.org/article/f9a548d2fde64e06af4dbda162bfa089
DOI:	10.3390/math8030403
Verfügbarkeit:	https://doi.org/10.3390/math8030403 https://doaj.org/article/f9a548d2fde64e06af4dbda162bfa089
Dokumentencode:	edsbas.92FD6F20
Datenbank:	BASE

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