On some degenerate non-local parabolic equation associated with the fractional p-Laplacian

Let ohm subset of R-N be an arbitrary bounded open set. We consider a degenerate parabolic equation associated to the fractional p-Laplace operator (-Delta)(p)(s) (p >= 2, s is an element of (0,1)) with the Dirichlet boundary condition and a monotone perturbation growing like vertical bar tau vertical bar(q-2) tau, q > p and with bad sign at infinity as vertical bar tau vertical bar -> infinity. We show the existence of locally-defined strong solutions to the problem with any initial condition mu(0) is an element of L-r(ohm) where r >= 2 satisfies r > N(q - p)/sp. Then, we prove that finite time blow-up is possible for these problems in the range of parameters provided for r, p, q and the initial datum mu(0).