Unique solvability of a nonlinear diffusion model with transmission boundary conditions

Models of tumor-induced capillary growth must accurately simulate the transport of growth factor from tumor site, through intersticial space, to a nearby capillary wall. In the spirit of recent works, the growth factor may be viewed as a diffusible chemical moving through a porous medium. Additionally, transmission between the capillary wall and intersticial space gives rise to a form of continuous delay condition at the boundary. Herein, we introduce a general nonlinear diffusion model, including such boundary conditions, and establish results on the unique solvability of the model.