A Class of Semilinear Parabolic Problems and Analytic Semigroups

Kazuaki Taira ()
Additional contact information
Kazuaki Taira: Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan

Mathematics, 2022, vol. 10, issue 22, 1-39

Abstract: (1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operators due to Lions–Peetre. (3) Results: We give a functional analytic proof of the C 2 compactness of a bounded regular solution orbit for semilinear parabolic problems with Dirichlet, Neumann and Robin boundary conditions. (4) Conclusions: As an application, we study the dynamics of a population inhabiting a strongly heterogeneous environment that is modeled by a class of diffusive logistic equations with Dirichlet and Neumann boundary conditions.

Keywords: semilinear initial boundary value problem; bounded regular solution orbit; compactness; analytic semigroup; diffusive logistic equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/22/4381/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/22/4381/ (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:10:y:2022:i:22:p:4381-:d:979069

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 ().