Critical Curves for Multidimensional Nonlinear Diffusion Equations Coupled by Nonlinear Boundary Sources

This paper is concerned with a class of nonlinear diffusion equations coupled by the nonlinear boundary sources on the exterior domain of the unit ball in \(\mathbb R^N\). We are interested in the critical curves which can describe the large time behavior of the solutions. It is shown that the critical global existence curve coincides with the critical Fujita curve for the system we considered.