A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source
Analysis of PDEs
2020-01-08 v1
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.
Keywords
Cite
@article{arxiv.1909.04577,
title = {A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source},
author = {Tian Xiang and Jiashan Zheng},
journal= {arXiv preprint arXiv:1909.04577},
year = {2020}
}
Comments
29 pages. To appear in Nonlinearity, 2019