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Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

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Carpio, Ana and Duro, Gema (2016) Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis. Nonlinear Analysis: Real World Applications, 30 . pp. 184-2012. ISSN 1468-1218

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Official URL: http://www.sciencedirect.com/science/article/pii/S1468121816000031


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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 ingiogenic 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


Item Type:Article
Uncontrolled Keywords:Kinetic model; Fokker-Planck; Integrodifferential; Angiogenesis
Subjects:Sciences > Mathematics
ID Code:37575
Deposited On:11 May 2016 11:17
Last Modified:31 May 2019 17:52

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