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Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours

Opened Access Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours

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Autor: Morales Rodrigo, Cristian
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2008-03
Publicado en: Mathematical and Computer Modelling, 47 (5-6), 604-613.
Tipo de documento: Artículo
Resumen: In this paper we consider a nonlinear system of differential equations arising in tumour invasion which has been proposed in [1] M.A.J. Chaplain and A.R.A. Anderson, Mathematical modelling of tissue invasion, in Cancer Modelling and Simulation, ed., L. Preziosi (Chapman & Hall/CRT, 2003), pp. 269–297. The system consists of two PDEs describing the evolution of tumour cells and proteases and an ODE which models the concentration of the extracellular matrix. We prove local existence and uniqueness of solutions in the class of Hölder spaces. The proof of local existence is done by Schauder’s fixed point theorem and for the uniqueness we use an idea from [2] H. Gajewski, K. Zacharias, Global behaviour of a reaction-diffusion system modelling chemotaxis, Math. Nachr. 195 (1998) 77–114.
Cita: Morales Rodrigo, C. (2008). Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours. Mathematical and Computer Modelling, 47 (5-6), 604-613.
Tamaño: 160.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/45004

DOI: 10.1016/j.mcm.2007.02.031

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