Global existence and blow-up for a nonlinear porous medium equation Original Research Article

In this paper, we investigate the positive solution of nonlinear nonlocal porous medium equation View the MathML source with homogeneous Dirichlet boundary condition and positive initial value u0(x), where m > 1, p, q ≥ 0. Under appropriate hypotheses, we establish the local existence and uniqueness of a positive classical solution, and obtain that the solution either exists globally or blows up in finite time by utilizing sub and super solution techniques. Furthermore, we yield the blow-up rate, i.e., there exist two positive constants C1, C2 such that where p+q > m > 1, T∗ is the blow-up time of u(x,t).