JournalsaihpcVol. 35, No. 5pp. 1321–1354

Uniform convergence for the incompressible limit of a tumor growth model

  • Inwon Kim

    Department of Mathematics, UCLA, Los Angeles, CA, 90095, United States
  • Olga Turanova

    Department of Mathematics, UCLA, Los Angeles, CA, 90095, United States
Uniform convergence for the incompressible limit of a tumor growth model cover
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Abstract

We study a model introduced by Perthame and Vauchelet [19] that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We adopt the viscosity solution approach to establish an optimal uniform convergence result of the tumor density as well as the pressure in the incompressible limit. The system lacks standard maximum principle, and thus modification of the usual approach is necessary.

Cite this article

Inwon Kim, Olga Turanova, Uniform convergence for the incompressible limit of a tumor growth model. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 5, pp. 1321–1354

DOI 10.1016/J.ANIHPC.2017.11.005