Well posedness of an integrodifferential kinetic model of Fokker–Planck type for angiogenesis. (August 2016)

• Record Type: Journal Article
• Authors: Carpio, Ana; Duro, Gema
• Is Part Of: Nonlinear analysis. Volume 30(2016)
• Page Start: 184
• Page End: 212
• Publication Date: 2016-08
• Subjects: Kinetic model -- Fokker–Planck -- Integrodifferential -- Angiogenesis; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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 the tumor induced angiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators.