Renormalized solutions to a chemotaxis system with consumption of chemoattractant
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Date
2019-03-11
Authors
Wang, Hengling
Li, Yuxiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the high-dimensional chemotaxis system with consumption of chemoattractant
ut = ∆u - ∇ ∙ (u∇v),
vt = ∆v - uv,
under homogeneous boundary conditions of Neumann type, in a bounded domain Ω ⊂ ℝn (n ≥ 4) with smooth boundary. We prove that if the initial data satisfy u0 ∈ C0(Ω̅) and v0 ∈ W1,q(Ω) for some q > n, this model possesses at least one global renormalized solution.
Description
Keywords
Keller-Segel model, Renormalized solutions, Entropy method
Citation
Wang, H., & Li, Y. (2019). Renormalized solutions to a chemotaxis system with consumption of chemoattractant. <i>Electronic Journal of Differential Equations, 2019</i>(38), pp. 1-19.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.