Well posedness of an angiogenesis related integrodifferential diffusion model

•Existence and uniqueness results for an angiogenesis related model are established.•A strategy to treat nonlocal anastomosis terms is proposed.•The nonlocal and nonlinear angiogenesis problem is approximable by iterative schemes.•Stability bounds allowing to control the solutions in terms of the data are given.•A basis to handle more realistic models including transport terms is set.

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficients allow us to generate sequences of approximate solutions. Comparison principles and integral equations provide uniform bounds ensuring some convergence properties for iterative schemes and providing stability bounds. Uniqueness follows from chained integral inequalities.