TY - JOUR
T1 - Nonexistence of global solutions of fractional diffusion equation with time-space nonlocal source
AU - Nabti, Abderrazak
AU - Alsaedi, Ahmed
AU - Kirane, Mokhtar
AU - Ahmad, Bashir
N1 - Funding Information:
The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, funded this project under grant no. (FP-16-42). Therefore the authors acknowledge with thanks DSR for technical and financial support. We also thank the reviewers for their constructive remarks on our work.
Funding Information:
The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia funded this project, under grant no. FP-16-42. Acknowledgements
Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Nonexistence of global solution
KW - Nonlocal source
KW - Test function
UR - https://www.scopus.com/pages/publications/85095566375
U2 - 10.1186/s13662-020-03083-0
DO - 10.1186/s13662-020-03083-0
M3 - Article
AN - SCOPUS:85095566375
SN - 1687-1839
VL - 2020
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 625
ER -