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On a chemotaxis model with competitive terms arising in angiogenesis

  • * Corresponding author: C. Morales-Rodrigo

    * Corresponding author: C. Morales-Rodrigo 
Supported by MINECO (Spain) grant MTM2015-69875P.
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  • In this paper we study an anti-angiogenic therapy model that deactivates the tumor angiogenic factors. The model consists of four parabolic equations and considers the chemotaxis and a logistic law for the endothelial cells and several boundary conditions, some of them are non homogeneous. We study the parabolic problem, proving the existence of a unique global positive solution for positive initial conditions, and the stationary problem, justifying the existence of one real number, an eigenvalue of a certain problem, which determines if the semi-trivial solutions are stable or unstable and the existence of a coexistence state.

    Mathematics Subject Classification: Primary: 35K45, 35K57; Secondary: 92C17.

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