%0 Journal Article %T Approximation by diffusion of renewal equations %+ Laboratoire d'Analyse, Topologie, Probabilités (LATP) %A Benabdallah, Assia %A Henry, Marie %< avec comité de lecture %@ 2254-3902 %J SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada %I Springer %V 56 %N 1 %P 5-34 %8 2011-09 %D 2011 %R 10.1007/BF03322595 %K approximation by diffusion of renewal equation %K size structured equation %K asymptotic behavior %K Mac-Kendrick Von Foerster equation %K transport equation %K Malthus parameter %K renewal equation %K semigroup %Z 92D25; 35A01, 35A02, 35A09, 35F15 %Z Mathematics [math]/Analysis of PDEs [math.AP] %Z Mathematics [math]/Dynamical Systems [math.DS]Journal articles %X In this paper, we consider an approximation by diffusion of a model of metastasis growth. We prove existence and uniqueness in L 1 of mild and classical solutions, in the sense of semigroup, and their convergence to mild and classical solutions of the original model, as the diffusion coefficient tends to zero. %G English %L hal-01305502 %U https://hal.science/hal-01305502 %~ LATP %~ CNRS %~ UNIV-AMU %~ INSMI %~ I2M %~ TDS-MACS %~ ANR