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Nonsymmetric traveling wave solution to a Hele-Shaw type tumor growth model

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arxiv 2404.16353 v2 pith:I6DYGOUN submitted 2024-04-25 math.AP

Yu Feng , Qingyou He , Jian-Guo Liu , Zhennan Zhou This is my paper · ORCID
classification math.AP
keywords modelgrowthtumorboundaryhele-shawinstabilitynonsymmetrictraveling
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We consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. The model is derived by taking the incompressible limit of porous medium type equations, and the boundary instability of this model was recently studied in \cite{feng2022tumor} using asymptotic analysis. In this paper, we further prove the existence of nonsymmetric traveling wave solutions to the model in a two dimensional tube-like domain, which reflect intrinsic boundary instability in tumor growth dynamics.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the incompressible limit of Keller-Segel system with volume-filling effects

    math.AP 2024-12 conditional novelty 7.0 of 10

    For the volume-filling Keller-Segel system, the incompressible limit is a Hele-Shaw free-boundary problem for K>1 and a hyperbolic Keller-Segel system for K≤1.

  2. Hele-Shaw limit of chemotaxis-Navier-Stokes flows

    math.AP 2025-06 conditional novelty 6.0 of 10

    For the chemotaxis-Navier-Stokes system with porous medium diffusion, as m→∞ the solutions converge to a Hele-Shaw free boundary problem whose pressure satisfies the complementarity relation P∞(ΔP∞ − ∇·(χ(c∞)∇c∞))=0.

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