Feature Papers in Functional Analysis and Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 1425

Special Issue Editor


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Guest Editor
Department of Mathematics, University of Antwerp, 2020 Antwerpen, Belgium
Interests: functional analyis; stochastic analyis; operator theory

Special Issue Information

Dear Colleagues,

In this Special Issue, papers in the following disciplines in mathematical analysis are welcome: functional analysis, operator theory and semigroups, (partial) differential equations, stochastic analysis, pseudo-differential operators including Boutet de Monvel calculus, boundary value problems, and Markov processes. Of course, it will also be a pleasure to receive papers with applications in these or related topics. In addition, articles that present interactions between the abovementioned fields are welcome, in particular results on the borderline between integral equations, functional analysis, and generation theorems for operator semigroups and Markov processes.

Prof. Dr. Jan Van Casteren
Guest Editor

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Keywords

  • function spaces
  • functional analysis
  • operator theory
  • operator semigroups
  • pseudo-differential operators
  • boutet de monvel calculus
  • Markov processes
  • martingale theory

Published Papers (1 paper)

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Research

39 pages, 766 KiB  
Article
A Class of Semilinear Parabolic Problems and Analytic Semigroups
by Kazuaki Taira
Mathematics 2022, 10(22), 4381; https://doi.org/10.3390/math10224381 - 21 Nov 2022
Viewed by 1136
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. [...] Read more.
(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 C2 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. Full article
(This article belongs to the Special Issue Feature Papers in Functional Analysis and Applications)
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