Fujita type results for quasilinear parabolic inequalities with nonlocal terms

In this paper we investigate the nonexistence of nonnegative solutions of parabolic inequalities, both of coercive type and of non coercive type, involving the p-Laplacian operator as well as the mean generalized curvature operator with a nonlocal term. In the non coercive case we obtain a Fujita type exponent, while in the coercive case we show that no such critical exponent exists. Our approach relies on nonlinear capacity estimates adapted to the nonlocal setting of our problems. No comparison results or maximum principles are required.