Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing

This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function , . The global existence of the unique boun...

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Bibliographic Details
Published in:Nonlinearity 2019-04, Vol.32 (4), p.1327-1351
Main Authors: Ahn, Jaewook, Yoon, Changwook
Format: Article
Language:English
Subjects:
chemotaxis
global existence
Lyapunov functional
motility function
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Summary:This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function , . The global existence of the unique bounded classical solutions is established without smallness of the initial data neither the convexity of the domain when , or , . In addition, we find the conditions on parameters, and , that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aaf513