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Passing to the limit 2D-1D in a model for metastatic growth

Abstract : We prove the convergence of a family of solutions to a two-dimensional transport equation with a nonlocal boundary condition modeling the evolution of a population of metastases. We show that when the data of the repartition along the boundary tends to a dirac mass then the solution of the associated problem converges and we derive a simple expression for the limit in term of the solution of a 1D equation. This result permits to improve the computational time needed to simulate the model.
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https://hal.archives-ouvertes.fr/hal-00521968
Contributor : Sebastien Benzekry <>
Submitted on : Wednesday, September 29, 2010 - 10:58:55 AM
Last modification on : Wednesday, December 9, 2020 - 3:13:03 AM
Long-term archiving on: : Thursday, December 30, 2010 - 2:41:14 AM

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Sebastien Benzekry. Passing to the limit 2D-1D in a model for metastatic growth. Journal of Biological Dynamics, Taylor & Francis Open, 2011, pp.10.1080/17513758.2011.568071. ⟨10.1080/17513758.2011.568071⟩. ⟨hal-00521968⟩

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