In this paper the authors 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, they 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, the authors 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
COLLI, PIERLUIGI;GILARDI, GIANNI MARIA;ROCCA, ELISABETTA;
2015-01-01
Abstract
In this paper the authors 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, they 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, the authors prove an error estimate leading also to the uniqueness result for the limit system.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
