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

Jiang, Ronghua; Zhou, Jun

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.

DEGENERATE parabolic equations; BLOWING up (Algebraic geometry); EQUATIONS

Communications on Pure & Applied Analysis, 2019, Vol 18, Issue 3, p1

1534-0392

Academic Journal

10.3934/cpaa.2019058