*ANNUNCIO DI SEMINARIO*
Il *14 aprile alle ore 15* nell'aula C del Dipartimento di Matematica, Universita' degli Studi di Milano, via Saldini 50, Milano si terrà un seminario sulla teoria dell'esistenza ed unicità di particolari equazioni integro-differenziali.
*Speaker: *Anna Carpio (Universitad Carlos III Madrid)
*Title:* *Well posedness of a kinetic model for angiogenesis*
*Abstract.* Tumor induced angiogenesis processes including the effect of stochastic motion, branching and merging of blood vessels can be described by coupling an integro-differential kinetic equation of Fokker-Planck type with a reaction-diffusion equation for the tumor induced angiogenic factor (TAF). The chemotactic force field depends on the gradient of the TAF equation contains the first velocity moment (flux of blood vessels). 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.