The Super-Diffusive Singular Perturbation Problem

Edgardo Alvarez and Carlos Lizama
Additional contact information
Edgardo Alvarez: Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla, Colombia
Carlos Lizama: Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

Mathematics, 2020, vol. 8, issue 3, 1-14

Abstract: In this paper we study a class of singularly perturbed defined abstract Cauchy problems. We investigate the singular perturbation problem ( P ? ) ? ? D t ? u ? ( t ) + u ? ? ( t ) = A u ? ( t ) , t ? [ 0 , T ] , 1 < ? < 2 , ? > 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 ? ) has a unique solution u ? ( t ) for each small ? > 0 . Moreover u ? ( t ) converges to u 0 ( t ) as ? ? 0 + , the unique solution of equation ( P ) .

Keywords: singular perturbation; fractional partial differential equations; analytic semigroup; super-diffusive processes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/3/403/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/3/403/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:3:p:403-:d:331407

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().