2018
DOI: 10.1186/s13661-018-1038-3
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Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

Abstract: We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption terms subject to null Dirichlet boundary condition. Based on a modified differential inequality technique, we establish some sufficient conditions to guarantee the existence of non-global solutions to the model and also derive the upper bounds for the blow-up time. Moreover, the lower bounds for the blow-up time are obtained under some appropriate measure in the whole-dimensional space (N ≥ 1).

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Cited by 6 publications
(2 citation statements)
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References 27 publications
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“…When m = 1a(x) = 1p = 0 Song [1] studied the lower bound of blow up time for solution of equation ( 6) with homogeneous Dirichlet and homogeneous Neumann boundary conditions; Liu [2] studied the lower bound of blow up time for the solution of equation ( 6) with nonlinear boundary conditions; Tang et al [3] has extended the results in equation ( 6) to higher dimensional cases, see Refs. [4][5][6][7] for other relevant achievements.…”
Section: Introductionmentioning
confidence: 99%
“…When m = 1a(x) = 1p = 0 Song [1] studied the lower bound of blow up time for solution of equation ( 6) with homogeneous Dirichlet and homogeneous Neumann boundary conditions; Liu [2] studied the lower bound of blow up time for the solution of equation ( 6) with nonlinear boundary conditions; Tang et al [3] has extended the results in equation ( 6) to higher dimensional cases, see Refs. [4][5][6][7] for other relevant achievements.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, there has been a great deal of literature on the global and blow-up solutions for nonlinear partial differential equations, for instance, in [1][2][3][4][5][6][7][8]. These works have contained a lot of interesting results about the global solutions, blow-up of solutions, bounds for the blow-up time, blow-up rates, and so on.…”
Section: Introductionmentioning
confidence: 99%