Existence of a Nontrivial Steady-State Solution to a Parabolic-Parabolic Chemotaxis System with Singular Sensitivity. (1st January 2019)

• Record Type: Journal Article
• Authors: Zhu, Yingjie
• Other Names: Luca Rodica Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-01-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/8140380
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.