Abstract
This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis {equation presented} in a smoothly bounded domain Ω Rn, n ≥ 1, under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function &gama;(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 {equation presented} In addition, we find the conditions on parameters, k and ϵ, that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.
Original language | English |
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Pages (from-to) | 1327-1351 |
Number of pages | 25 |
Journal | Nonlinearity |
Volume | 32 |
Issue number | 4 |
DOIs | |
State | Published - 12 Mar 2019 |
Keywords
- chemotaxis
- global existence
- Lyapunov functional
- motility function