We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time. For blowing up solutions, we find asymptotic bounds for the blow-up rate.
"Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms." Abstr. Appl. Anal. 2018 1 - 10, 2018. https://doi.org/10.1155/2018/3906431