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.
Highlights
Acid-mediated tumor invasion model confines a mechanism linking altered glucose metabolism with the ability of tumor cells to form invasive cancers
Glucose metabolism and increased glucose uptake observed in the majority of clinical cancers which are critical for development of the invasive phenotype
Acidification of the tumor micro environment is shown by Gatenby et al [15] and Martin et al [17] to increase invasiveness and metastasis of cancer cells using mathematical model
Summary
Acid-mediated tumor invasion model confines a mechanism linking altered glucose metabolism with the ability of tumor cells to form invasive cancers. Local and global existence of solutions of the model governed by acid-mediated tumor invasion established in [20]. Acid-mediated invasion model for tumor-stromal interactions under no flux boundary condition is concerned in [16] and the global existence and uniqueness proved using contraction mapping principle. Existence of renormalized and entropy solutions for the system of parabolic equations concerned, only few papers available in the literature, see, [3, 4, 24, 25]. In contrast to the above mentioned papers, in this work, the main novel point is to establish the existence of renormalized and entropy solutions of the model governed by the acid-mediated tumor growth under no growth conditions and integrable data.
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