A free boundary tumor model with time dependent nutritional supply. (June 2020)

• Record Type: Journal Article
• Authors: Sun, Wenlong; Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: Free boundary problem -- Tumor growth -- Long time dynamics -- Transient solution -- Steady-state solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103063
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equation describing the evolution of the tumor size. First the global existence and uniqueness of a transient solution is established under some general conditions. Then with additional regularity assumptions on the consumption and proliferation rates, the existence and uniqueness of steady-state solutions is obtained. Furthermore the convergence of the transient solutions toward the steady-state solution is verified. Finally the long time behavior of the solutions is investigated by transforming the time-dependent domain to a fixed domain.