A reaction–diffusion system with mixed-type coupling

Blow-up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition

“…They established local existence, global existence and nonexistence of solutions and discussed the blow up properties of solutions. Similar results can be seen in [23,24,[26][27][28][29][30].…”

“…On the other hand, due to the appearance of the nonlocal boundary condition, the properties of solution heavily depend on the weight function uðx; yÞ as well. Motivated by the above cited works and the references [18,22,[25][26][27][28][29][30], in this paper we deal with a nonlinear parabolic equation subject to nonlocal boundary conditions and with nonlocal sources. By means of a sub-super-solution method, we obtained conditions which guarantee the solutions having global existence or blowing up in finite time (see Section 3 for details).…”