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Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production.
- Source :
-
Journal of Mathematical Analysis & Applications . Jun2019, Vol. 474 Issue 1, p733-747. 15p. - Publication Year :
- 2019
-
Abstract
- Abstract This work is concerned with a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production: u t = ∇ ⋅ ((1 + u) − α ∇ u) − ∇ ⋅ (u (1 + u) β − 1 ∇ v) + f (u) , v t = Δ v − v + u γ , with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain, where α , β ∈ R and γ > 0. The logistic type source term f (u) satisfies that either f (u) ≡ 0 or f (u) = r u − μ u k with r ∈ R , μ > 0 and k > 1. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameters conditions, which improves the known results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 474
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134664651
- Full Text :
- https://doi.org/10.1016/j.jmaa.2019.01.076