Uniqueness and Nonlinear Stability of Positive Entire Solutions in Parabolic-Parabolic Chemotaxis Models With Logistic Source on Bounded Heterogeneous Environments

Authors

• Tahir Bachar Issa, San Jose State UniversityFollow

Publication Date

4-15-2026

Document Type

Article

Publication Title

Proceedings of the American Mathematical Society Series B

Volume

13

Issue

1

DOI

10.1090/bproc/277

First Page

44

Last Page

58

Abstract

This paper studies the asymptotic behavior of solutions of the parabolic-parabolic chemotaxis model with logistic-type sources in heterogeneous bounded domains: (formula present) We find parameter regions in which the system has a unique positive entire solution, which is globally asymptotically stable. More precisely, under suitable assumptions on the model’s parameters, the system has a unique positive entire solution (u∗(t, x), v∗(t, x)) such that for any u0 ∈ C⁰(Ω̅), v0 ∈ W^1,∞(Ω̅) with u0, v0 ≥ 0 and u0 ≢ 0, the global classical solution (u(t, x; t0, u0, v0), v(t, x; t0, u0, v0)) of (∗) satisfies (formula present).

Keywords

comparison principle, entire solutions, Fully parabolic chemotaxis model, uniqueness and stability

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Department

Mathematics and Statistics

Recommended Citation

Tahir Bachar Issa. "Uniqueness and Nonlinear Stability of Positive Entire Solutions in Parabolic-Parabolic Chemotaxis Models With Logistic Source on Bounded Heterogeneous Environments" Proceedings of the American Mathematical Society Series B (2026): 44-58. https://doi.org/10.1090/bproc/277