  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.
