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Blow-up and global existence of solutions to a parabolic equation associated with the fraction p-Laplacian

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This work is supported by NSFC grant 11201380 and the Basic and Advanced Research Project of CQC-STC grant cstc2016jcyjA0018

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  • We consider a nonlocal parabolic equation associated with the fractional p-laplace operator, which was studied by Gal and Warm in [On some degenerate non-local parabolic equation associated with the fractional p-Laplacian. Dyn. Partial Differ. Equ., 14(1): 47-77, 2017]. By exploiting the boundary condition and the variational structure of the equation, according to the size of the initial dada, we prove the finite time blow-up, global existence, vacuum isolating phenomenon of the solutions. Furthermore, the upper and lower bounds of the blow-up time for blow-up solutions are also studied. The results generalize the results got by Gal and Warm.

    Mathematics Subject Classification: 35R11, 35K55, 35K65.


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