Reaction-Difusion Model of Early Carcinogenesis: The Effects of Influx of Mutated Cells

DOI10.1051/mmnp:2008043zbMath1337.92047OpenAlexW2167227864MaRDI QIDQ2786777

Marek Kimmel, Anna Marciniak-Czochra

Publication date: 23 February 2016

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/mmnp:2008043

zbMATH Keywords

pattern formationreaction-diffusion equationscooperationcancer modellingspike solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Medical applications (general) (92C50) Cell biology (92C37)

Related Items (12)

Shadow limit using renormalization group method and center manifold method ⋮ Finite-time blowup of solutions to some activator-inhibitor systems ⋮ Dynamical spike solutions in a nonlocal model of pattern formation ⋮ Unstable patterns in reaction-diffusion model of early carcinogenesis ⋮ An averaging principle for fast diffusions in domains separated by semi-permeable membranes ⋮ How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems ⋮ On the robustness of discontinuous patterns in degenerate reaction-diffusion systems with perturbed hysteresis ⋮ Irregular convergence of mild solutions of semilinear equations ⋮ Modeling Diffusion in Thin 2D Layers Separated by a Semipermeable Membrane ⋮ Instability of Turing patterns in reaction-diffusion-ODE systems ⋮ Spike patterns in a reaction–diffusion ODE model with Turing instability ⋮ Singular perturbations involving fast diffusion

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