Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

Abstract

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 $N\geq1$).

Keywords

• Porous medium equation
• Weighted nonlocal source
• Inner absorption
• Bounds for the blow-up time