Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion

DOI10.3934/MBE.2016.13.193zbMath1326.35407OpenAlexW2416568737WikidataQ40098275 ScholiaQ40098275MaRDI QIDQ746560

D. Kharzeev

Publication date: 16 October 2015

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mbe.2016.13.193

zbMATH Keywords

existence of solutionsreaction diffusion equationsnumerical simulationsmorphogenesissteady states

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (6)

Mathematical analysis of a non-local mixed ODE-PDE model for tumor invasion and chemotherapy ⋮ Solvability of the acid-mediated tumor growth model with nonlinear acid production term ⋮ Global stability of a PDE-ODE model for acid-mediated tumor invasion ⋮ Computational solution of an acid-mediated tumor-growth radial model under logistic growth regimes for normal and cancer cells ⋮ Propagation fronts in a simplified model of tumor growth with degenerate cross-dependent self-diffusivity ⋮ RENORMALIZED AND ENTROPY SOLUTIONS OF TUMOR GROWTH MODEL WITH NONLINEAR ACID PRODUCTION

Cites Work

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• On a comparison method to reaction-diffusion systems and its applications to chemotaxis
• Global existence for a haptotaxis model of cancer invasion with tissue remodeling
• Mathematical biology. Vol. 1: An introduction.
• Slow and fast invasion waves in a model of acid-mediated tumour growth
• A general reaction-diffusion model of acidity in cancer invasion

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