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A Hele-Shaw Problem for Tumor Growth

Abstract : We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra source term describing the evolution of the number density of cancerous cells. We prove that such limit solutions solve a free boundary problem of Hele-Shaw type. We also obtain regularity properties, both for the solution and for its free boundary. The main new difficulty arises from the competition between the growth due to the source, which keeps the initial singularities, and the free boundary which invades the domain with a regularizing effect. New islands can be generated at singular times.
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Contributor : Benoît Perthame <>
Submitted on : Thursday, December 10, 2015 - 12:23:49 PM
Last modification on : Friday, March 27, 2020 - 3:01:19 AM
Document(s) archivé(s) le : Friday, March 11, 2016 - 3:01:11 PM


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  • HAL Id : hal-01241309, version 1
  • ARXIV : 1512.06995


Antoine Mellet, Benoît Perthame, Fernando Quirós. A Hele-Shaw Problem for Tumor Growth. Journal of Functional Analysis, Elsevier, 2017, 273, pp.3061-3093. ⟨hal-01241309⟩



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