Existence of a Nontrivial Steady-State Solution to a Parabolic-Parabolic Chemotaxis System with Singular Sensitivity

Existence of a Nontrivial Steady-State Solution to a Parabolic-Parabolic Chemotaxis System with Singular Sensitivity

This paper establishes the existence of a nontrivial steady-state solution to a parabolic-parabolic coupled system with singular (or logarithmic) sensitivity and nonlinear source arising from chemotaxis. The proofs mainly rely on the maximum principle, the implicit function theorem, and the Hopf bif...

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Veröffentlicht in:Discrete dynamics in nature and society 2019, Vol.2019 (2019), p.1-6
1. Verfasser: Zhu, Yingjie
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Bifurcation theory
Hopf bifurcation
Maximum principle
Motility
Population growth
Sensitivity
Steady state
Theorems
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Zusammenfassung:This paper establishes the existence of a nontrivial steady-state solution to a parabolic-parabolic coupled system with singular (or logarithmic) sensitivity and nonlinear source arising from chemotaxis. The proofs mainly rely on the maximum principle, the implicit function theorem, and the Hopf bifurcation theorem.
ISSN:1026-0226
1607-887X
DOI:10.1155/2019/8140380