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

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• 作者：Ana Carpio^a ; ^{carpio@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author} ; Gema Duro^b ; ^{gema.duro@uam.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Kinetic model ; Fokker&ndash ; Planck ; Integrodifferential ; Angiogenesis
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：30
• 期：Complete
• 页码：184-212
• 全文大小：742 K

文摘

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.