Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing
- Authors
- Ahn, Jaewook; Yoon, Changwook
- Issue Date
- 4월-2019
- Publisher
- IOP PUBLISHING LTD
- Keywords
- chemotaxis; motility function; global existence; Lyapunov functional
- Citation
- NONLINEARITY, v.32, no.4, pp.1327 - 1351
- Indexed
- SCIE
SCOPUS
- Journal Title
- NONLINEARITY
- Volume
- 32
- Number
- 4
- Start Page
- 1327
- End Page
- 1351
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/66569
- DOI
- 10.1088/1361-6544/aaf513
- ISSN
- 0951-7715
- Abstract
- This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis u(t) = Delta(gamma(v)u), 0 = epsilon Delta v - v + u in a smoothly bounded domain Omega subset of R-n, n >= 1, under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function gamma(v) = v(-k), k > 0. The global existence of the unique bounded classical solutions is established without smallness of the initial data neither the convexity of the domain when n <= 2, k > 0 or n >= 3, k < 2/n-2. In addition, we find the conditions on parameters, k and epsilon, that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.
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