RT Book, Section
T1 Well posedness and numerical solution of kinetic models for angiogenesis
A1 Carpio, Ana
A1 Cebrián, Elena
A1 Duro, Gema
AB Angiogenesis processes including the effect of stochastic branching and spread of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker-Planck type with a diffusion equation for the angiogenic factor. Well posedness studies underline the importance of preserving positivity when constructing approximate solutions. We devise order one positivity preserving schemes for a reduced model and show that soliton-like asymptotic solutions are correctly captured. We also find good agreement with the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages. Higher order positivity preserving schemes can be devised combining WENO and SSP procedures.
PB Universidad de Oviedo
SN 9788418482212
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/8839
UL https://hdl.handle.net/20.500.14352/8839
LA eng
NO [1] LL Bonilla, A Carpio, M Carretero, G Duro, M Negreanu, F Terragni. A convergent numerical scheme for integrodifferential kinetic models of angiogenesis. J. Comput. Phys., 375:1270–1294, 2018.[2] V. Capasso, D. Morale, G. Facchetti. Randomness in self-organized phenomena. A case study: Retinal angiogenesis. BioSystems, 112:292-297, 2013.[3] A. Carpio, G. Duro Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis. Nonlinear Analysis-Real World Applications, 30:184-212, 2016.[4] A. Carpio, G. Duro, M. Negreanu, Constructing solutions for a kinetic model of angiogenesis in annular domains Applied Mathematical Modelling, 45:303-322, 2017.[5] A. Carpio, E. Cebrián, High order positivity preserving schemes for kinetic models of angiogenesis. Preprint, 2020.[6] C.W. Shu, Total-variation diminishing time discretizations, SIAM J. Sci. Statist. Comput. 9, 1073-1084, 1988.[7] X. Zhang, Y. Liu, C.W. Shu. Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations. SIAM J. Sci. Comput., 34:A627-A658, 2012.
NO Coordinadores: Rafael Gallego, Mariano Mateos (2021), Proceedings of the XXVI Congreso de EcuacionesDiferenciales y Aplicaciones / XVI Congreso de Matemática Aplicada. Universidad de Oviedo.
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 7 may 2024