Xiaoying (Maggie) Han, Auburn University
Authors: Wenlong Sun, Tomas Caraballo, Xiaoying Han, Peter Kloeden
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs

A non-autonomous free boundary model for tumor growth will be introduced. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equations describing the evolution of the tumor size. Global existence and uniqueness of solutions, existence and uniqueness of steady state solutions will be presented first. Then convergence of the transient solutions toward the steady state solution, as well as the long time dynamics of the solutions will be discussed.

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