Nonlinear Evolution Equations and Their Application to Chemotaxis Models

Akisato Kubo, Hiroki Hoshino

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Recently, we have investigated the global existence in time and asymptotic profile of solutions of some nonlinear evolution equations with strong dissipation and proliferation arising in mathematical biology. In this chapter, we improve the asymptotic behaviour of the solution to a simpler equation so that its derivative with respect to t converges exponentially to a constant steady state. We apply our result to a chemotaxis model and show the global existence in time and such exponential convergence property of the solution.

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer International Publishing
Pages337-347
Number of pages11
DOIs
Publication statusPublished - 01-01-2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Fingerprint

Chemotaxis
Nonlinear Evolution Equations
Global Existence
Mathematical Biology
Asymptotic Profile
Exponential Convergence
Proliferation
Convergence Properties
Dissipation
Asymptotic Behavior
Converge
Derivative
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Kubo, A., & Hoshino, H. (2019). Nonlinear Evolution Equations and Their Application to Chemotaxis Models. In Trends in Mathematics (pp. 337-347). (Trends in Mathematics). Springer International Publishing. https://doi.org/10.1007/978-3-030-04459-6_32
Kubo, Akisato ; Hoshino, Hiroki. / Nonlinear Evolution Equations and Their Application to Chemotaxis Models. Trends in Mathematics. Springer International Publishing, 2019. pp. 337-347 (Trends in Mathematics).
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Kubo, A & Hoshino, H 2019, Nonlinear Evolution Equations and Their Application to Chemotaxis Models. in Trends in Mathematics. Trends in Mathematics, Springer International Publishing, pp. 337-347. https://doi.org/10.1007/978-3-030-04459-6_32

Nonlinear Evolution Equations and Their Application to Chemotaxis Models. / Kubo, Akisato; Hoshino, Hiroki.

Trends in Mathematics. Springer International Publishing, 2019. p. 337-347 (Trends in Mathematics).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Kubo A, Hoshino H. Nonlinear Evolution Equations and Their Application to Chemotaxis Models. In Trends in Mathematics. Springer International Publishing. 2019. p. 337-347. (Trends in Mathematics). https://doi.org/10.1007/978-3-030-04459-6_32