title: 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 non-local boundary condition modelling the evolution of a population of metastases. We show that when the data of the repartition along the boundary tend to a Dirac mass, then the solution of the associated problem converges and we derive a simple expression for the limit in terms of the solution of a 1D equation. This result permits us to improve the computational time needed to simulate the model.
authors.affiliation: Université de Provence , Technopôle Château-Gombert, 39 rue F. Joliot Curie, Marseille cedex 13 , France. benzekry@phare.normalesup.org
authors.forename: Sebastien
authors.initials: S
authors.lastname: Benzekry
mesh_terms: D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009362:Neoplasm Metastasis / Q000473:pathology*