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We present an iterative technique to construct stable solutions for an angiogenesis model set in an annular region. Branching, anastomosis and extension of blood vessel tips is described by an integrodifferential kinetic equation of Fokker-Planc[...]texto impreso
Bonilla, Luis L. ; Carpio, Ana ; Carretero, Manuel ; Duro, Gema ; Negreanu, Mihaela ; Terragni, Filippo | Elsevier | 2018-12-15We study a robust finite difference scheme for integrodifferential kinetic systems of Fokker-Planck type modeling tumor driven blood vessel growth. The scheme is of order one and enjoys positivity features. We analyze stability and convergence p[...]texto impreso
Explosive instabilities in spatially discrete reaction-diffusion systems are studied. We identify classes of initial data developing singularities in finite time and obtain predictions of the blow-up times, whose accuracy is checked by compariso[...]texto impreso
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficie[...]texto impreso
Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for[...]
