On the long time behavior of a tumor growth model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Miranville, Alain^1,2,3  Rocca, Elisabetta^4,5  Schimperna, Giulio^4,5 

[1] Univ Poitiers, Lab Math & Applicat, UMR CNRS 7348, Equipe DACTIM MIS,SP2MI, Blvd Marie & Pierre Curie, F-86962 Futuroscope, France

[2] Fudan Univ, Shanghai, Peoples R China

[3] Xiamen Univ, Sch Math Sci, Xiamen, Fujian, Peoples R China

[4] Univ Pavia, Dipartimento Matemat, Via Ferrata 5, I-27100 Pavia, Italy

[5] CNR, IMATI, Via Ferrata 5, I-27100 Pavia, Italy

关键词: Tumor growth;    Phase field model;    Initial-boundary value problem;    Well-posedness;    Dissipativity;    Global attractor;   

DOI  :  10.1016/j.jde.2019.03.028

来源: Elsevier

【 摘 要 】

We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type equation for the tumor phase coupled with a reaction-diffusion equation for the nutrient concentration. We prove that, under physically motivated assumptions on parameters and data, the corresponding initial-boundary value problem generates a dissipative dynamical system that admits the global attractor in a proper phase space. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free