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- W3132752095 abstract "We consider the differential inequality with a nonlinear memory ∂tu−Δu≥1Γ(σ)∫0t(t−s)σ−1|u(s,x)|pds+w(x),t>0,x∈R+N, where N≥2, p>1, σ>0, and w⁄≡0. Under certain conditions on the initial value and the inhomogeneous term w, we show that the Fujita critical exponent is given by pσ∗=∞, for all σ>0. Next, we consider the limit case of the above problem as σ→0+, i.e. ∂tu−Δu≥|u|p+w(x),t>0,x∈R+N. A discontinuity phenomenon of the critical exponent is observed. Namely, we show that the Fujita critical exponent for the limit problem is equal to N+1N−1, which is different to limσ→0+pσ∗." @default.
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- W3132752095 date "2021-07-01" @default.
- W3132752095 modified "2023-09-23" @default.
- W3132752095 title "On the critical behavior for inhomogeneous parabolic differential inequalities in the half-space" @default.
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- W3132752095 doi "https://doi.org/10.1016/j.aml.2021.107099" @default.
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