Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
type: Item
instance of: scholarly article
title: Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
zbMATH Open document ID: 1332.35369
author: N. E. Zubov
published in: Journal of Differential Equations
publication date: 2015-12-07T00:00:00Z
review text: The authors study a nonlinear singular chemotaxis parabolic system (with a logarithmic sensitivity function) modeling the onset of tumor angiogenesis in two and three dimensional space. By a Cole-Hopf type transformation, the singular chemotaxis system is converted into a nonsingular hyperbolic system \[ \begin{aligned} u_t -\Delta u & =\nabla\cdot(u\boldsymbol{v}), \\ \boldsymbol{v}_t-\varepsilon\Delta \boldsymbol{v} & =\nabla(-\varepsilon|\boldsymbol{v}|^2+u). \end{aligned} \] The global existence, asymptotic decay rates and diffusion convergence rate of solutions (when \(\varepsilon\to 0\)) with the initial data which are small perturbations of constant states are shown by the method of energy estimates. An interesting feature of those results is revealing a hidden interactive dissipation structure in the system by which the energy dissipation is established.
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6517070
zbMATH Keywords: singular chemotaxis
zbMATH Keywords: tumor angiogenesis
zbMATH Keywords: energy estimates
zbMATH Keywords: decay estimates
reviewed by: Piotr Biler
MaRDI profile type: Publication
full work available at URL: j.jde.2015.09.063
OpenAlex ID: W2195359973
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DOI: 10.1016/J.JDE.2015.09.063
description: scientific article; zbMATH DE number 6517070