Renormalized and Entropy Solutions of Tumor Growth Model with Nonlinear Acid Production

Abstract

This paper establishes the existence of renormalized and entropy solutions for a system of nonlinear reaction-diffusion equations which describes the tumor growth along with acidification and interaction. Under the assumptions of L¹ data and no growth conditions with zero Dirichlet boundary conditions, we prove the existence of renormalized and entropy solutions for the considered mathematical model.

Keywords:

• acid-mediated tumor growth
• renormalized solution
• entropy solution

AMS Subject Classification:

• 35K57
• 35K65
• 92D25
• 35D99