A free boundary tumor model with time dependent nutritional supply

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Wenlong Sun, Tomás Caraballo, Xiaoying Han, Peter E. KloedenAbstractA 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.

Source: Nonlinear Analysis: Real World Applications - November 13, 2019 Category: Research Source Type: research