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Journal Articles Journal of Biological Dynamics Year : 2011

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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Dates and versions

hal-00521968 , version 1 (29-09-2010)

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