Abstract
A free boundary model for tumor growth with time dependent nutritional supply and infinite time delays is studied. The governing system 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 according to Banach fixed point theorem under some general conditions. Then with additional regularity assumptions on the consumption and net proliferation rates, the existence and uniqueness of a steady-state solution is shown and the convergence of the transient solution onto the steady-state solution is proved.
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Acknowledgements
The authors would like to express their gratitude to Professor Tomás Caraballo for suggestive discussions, and to the anonymous referees for their comments.
Funding
This study was partially funded by the China Scholarship Council, NSF of China (Grant no. 11571125), Simons Foundation (Collaboration Grants for Mathematicians no. 429717), and Ministerio de Economia y Competitividad, Spain, FEDER European Community (Grant no. MTM2015-63723-P).
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Dedicated to Prof. Michel Chipot on the occasion of his 70th birthday.
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Sun, W., Han, X. & Kloeden, P. Analysis of a nonautonomous free boundary tumor model with infinite time delays. J Elliptic Parabol Equ 6, 5–25 (2020). https://doi.org/10.1007/s41808-020-00053-1
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DOI: https://doi.org/10.1007/s41808-020-00053-1