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Y. Li. K. Lin, C. Mu, Boundedness and asymptotic behavior of solutions to a chemotaxis haptotaxis model in high dimensions, Appl. Math. Lett., 50(2015), 91-97.

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Article

Existence and Uniqueness of a Chemotaxis System Influenced by Cancer Cells

1College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China


International Journal of Partial Differential Equations and Applications. 2020, Vol. 7 No. 1, 1-7
DOI: 10.12691/ijpdea-7-1-1
Copyright © 2020 Science and Education Publishing

Cite this paper:
Gang Li, Hui Min Hu, Xi Chen, Fei Da Jiang. Existence and Uniqueness of a Chemotaxis System Influenced by Cancer Cells. International Journal of Partial Differential Equations and Applications. 2020; 7(1):1-7. doi: 10.12691/ijpdea-7-1-1.

Correspondence to: Fei  Da Jiang, College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. Email: jfd2001@163.com

Abstract

We present a mathematical analysis of a reaction-diffusion model in a bounded open domain which describes vascular endothelial growth factor(VEGF), endothelial cells and oxygen. We use the parabolic theory to prove the existence of the solution in the function space under the homogeneous Neumann conditions. Then we get the existence of nonnegative solution in by using the global Schauder estimation.

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