LONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS

In order to accurately simulate the transport of growth factor from tumor site into a nearby capillary wall, a recently introduced model of tumor-induced capillary growth incorporates a new form of transmission boundary flux. Growth factor emitted from the tumor may be viewed as a diffusible chemical moving through intersticial space, which is represented as a porous medium. Transmission between the capillary wall and intersticial space gives rise to a type of continuous delay/memory condition at the boundary. Herein, we establish results on global solvability and blow up in finite time for a general nonlinear diffusion model, including such transmission boundary conditions. Although the model appears more closely aligned with models involving nonlinear flux conditions at the boundary, these results bear notable similarities to those with Dirichlet boundary conditions.