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 .

中文翻译：

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带梯度项的抛物线不等式的 Fujita 类型结果

摘要 在本文中，我们给出了具有扩散项和耗散项的强 p 矫顽拟线性抛物线微分不等式的一些 Fujita 型结果，其原型为 ut − Δ pu ≥ a ( x ) uq − b ( x ) um | ∇ 你 | s in RN × R + , u ≥ 0 , u ( x , 0 ) = u 0 ( x ) ≥ 0 in RN , 其中 p > 1 , q > 0 , 0 ≤ mq , 0 s ≤ p ( q − m ) / ( q + 1 ) 和 a , b 非负权重，可以是奇异的或退化的。我们证明了 Fujita 型指数 q F 的存在性，使得当 qq F 时不等式的解不存在。