We concern with the extinction behavior of the solution for a parabolic $ p $-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods, we obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.
Citation: Dengming Liu, Luo Yang. Extinction behavior for a parabolic $ p $-Laplacian equation with gradient source and singular potential[J]. AIMS Mathematics, 2022, 7(1): 915-924. doi: 10.3934/math.2022054
We concern with the extinction behavior of the solution for a parabolic $ p $-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods, we obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.
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Dengming Liu, Luo Yang. Extinction behavior for a parabolic $ p $-Laplacian equation with gradient source and singular potential[J]. AIMS Mathematics, 2022, 7(1): 915-924. doi: 10.3934/math.2022054
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