Málstofa í stærðfræði
Fyrirlesari: Ana Carpio, Universidad Complutense de Madrid
Titill: Well posedness of a kinetic model for angiogenesis
Staðsetning: VR-II, 158.
Tími: Fimmtudagur 9. júlí, klukkan 15:00-16:00.
Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling an integrodifferential kinetic equation of Fokker-Planck type with a diffusion equation for the tumor induced angiogenic factor. The chemotactic force field depends on the first velocity moment (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. Our theory combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity moments and compactness results for this type of kinetic and parabolic operators.