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- W3199811042 abstract "We study fractional parabolic equations with indefinite nonlinearities∂u∂t(x,t)+(−Δ)su(x,t)=x1up(x,t),(x,t)∈Rn×R, where 0<s<1 and 1<p<∞. We first prove that all positive bounded solutions are monotone increasing along the x1 direction. Based on this we derive a contradiction and hence obtain non-existence of solutions. These monotonicity and nonexistence results are crucial tools in a priori estimates and complete blow-up for fractional parabolic equations in bounded domains. To this end, we introduce several new ideas and developed a systematic approach which may also be applied to investigate qualitative properties of solutions for many other fractional parabolic problems." @default.
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- W3199811042 date "2021-12-01" @default.
- W3199811042 modified "2023-10-18" @default.
- W3199811042 title "Nonexistence of solutions for indefinite fractional parabolic equations" @default.
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- W3199811042 doi "https://doi.org/10.1016/j.aim.2021.108018" @default.
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