Abstract:

In this paper, we explore the blow-up of solutions to a class of nonlocal porous medium systems with space-dependent coefficients and inner absorption terms under nonlinear boundary conditions in ${\mathbb{R}}^{n}\left(n \geqslant 3\right)$ . By constructing an energy expression and using the differential inequality technique, we obtain sufficient conditions for the global existence of solutions to the problem. Then, upper bound and lower bound estimates of the blow-up time are derived by means of the Sobolev inequalities and other differential methods when blow-up occurs.

Key words: blow-up, porous medium system, space-dependent coefficient, inner absorption term