A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source

Abstract

We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of cancer invasion with/without kinetic source in a 2D bounded and smooth domain. For a large class of cell kinetic sources including zero source and sub-logistic sources, we detect an explicit condition involving the chemotactic strength, the asymptotic "damping" rate, and the initial mass of cells to ensure uniform-in-time boundedness for the corresponding Neumann problem. Our finding significantly improves existing 2D global existence and boundedness in related chemotaxis-/haptotaxis systems.

arXiv comment29 pages. To appear in Nonlinearity, 2019

References in corpus (8)

• Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
• How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
• Boundedness in a three-dimensional chemotaxis-haptotaxis model
• Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
• Boundedness in a two-dimensional chemotaxis-haptotaxis system
• Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
• Boundedness of solution of a parabolic--ODE--parabolic chemotaxis--haptotaxis model with (generalized) logistic source
• Boundedness and exponential convergence of a chemotaxis model for tumor invasion

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