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).

Lower Bounds of Blow Up Time for a Class of Slow Reaction Diffusion Equations with Inner Absorption Terms

“…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.…”

Global and blow-up solutions for a nonlinear reaction diffusion equation with Robin boundary conditions

“…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.…”