Fujita type results for parabolic inequalities with gradient terms

Abstract In this paper we give some Fujita type results for strongly p-coercive quasilinear parabolic differential inequalities with both a diffusion term and a dissipative term, whose prototype is given by u t − Δ p u ≥ a ( x ) u q − b ( x ) u m | ∇ u | s in R N × R + , u ≥ 0 , u ( x , 0 ) = u 0 ( x ) ≥ 0 in R N , where p > 1 , q > 0 , 0 ≤ m q , 0 s ≤ p ( q − m ) / ( q + 1 ) and a , b nonnegative weights which could be singular or degenerate. We prove the existence of Fujita type exponents q F , such that nonexistence of solutions for the inequality occurs when q q F .