Nonexistence of global solutions of fractional diffusion equation with time-space nonlocal source

Abderrazak Nabti, Ahmed Alsaedi, Mokhtar Kirane, Bashir Ahmad

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Abstract

We prove the nonexistence of solutions of the fractional diffusion equation with time-space nonlocal sourceut+(−Δ)β2u=(1+|x|)γ∫0t(t−s)α−1|u|p∥ν1q(x)u∥qrds for (x, t) ∈ RN× (0 , ∞ ) with initial data u(x,0)=u0(x)∈Lloc1(RN), where p, q, r> 1 , q(p+ r) > q+ r, 0 < γ≤ 2 , 0 < α< 1 , 0 < β≤ 2 , (−Δ)β2 stands for the fractional Laplacian operator of order β, the weight function ν(x) is positive and singular at the origin, and ∥ ⋅ ∥ q is the norm of Lq space.

Original languageBritish English
Article number625
JournalAdvances in Difference Equations
Volume2020
Issue number1
DOIs
StatePublished - 1 Dec 2020

Keywords

  • Nonexistence of global solution
  • Nonlocal source
  • Test function

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