In this paper we perform an asymptotic analysis for two different vanishing viscosity coefficients occurring in a phase field system of Cahn-Hilliard type that was recently introduced in order to approximate a tumor growth model. In particular, we extend some recent results obtained in Colli et al. (2015), letting the two positive viscosity parameters tend to zero independently from each other and weakening the conditions on the initial data in such a way as to maintain the nonlinearities of the PDE system as general as possible. Finally, under proper growth conditions on the interaction potential, we prove an error estimate leading also to the uniqueness result for the limit system.

Vanishing viscosities and error estimate for a Cahn-Hilliard type phase field system related to tumor growth

P Colli;G Gilardi;E Rocca;
2015

Abstract

In this paper we perform an asymptotic analysis for two different vanishing viscosity coefficients occurring in a phase field system of Cahn-Hilliard type that was recently introduced in order to approximate a tumor growth model. In particular, we extend some recent results obtained in Colli et al. (2015), letting the two positive viscosity parameters tend to zero independently from each other and weakening the conditions on the initial data in such a way as to maintain the nonlinearities of the PDE system as general as possible. Finally, under proper growth conditions on the interaction potential, we prove an error estimate leading also to the uniqueness result for the limit system.
2015
Istituto di Matematica Applicata e Tecnologie Informatiche - IMATI -
Asymptotic analysis
Cahn-Hilliard System
Error estimates
Reaction-diffusion equation
Tumor growth
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/315999
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