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A Class of Semilinear Parabolic Problems and Analytic Semigroups

Author

Listed:
  • Kazuaki Taira

    (Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan)

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.

Suggested Citation

  • Kazuaki Taira, 2022. "A Class of Semilinear Parabolic Problems and Analytic Semigroups," Mathematics, MDPI, vol. 10(22), pages 1-39, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4381-:d:979069
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