Article ID Journal Published Year Pages File Type
4627008 Applied Mathematics and Computation 2015 5 Pages PDF
Abstract

This paper deals with a degenerate nonlinear diffusion equation with gradient absorption. We at first determine finite time blow-up of solutions both in the L∞L∞-norm and an integral measure, and then estimate a lower bound of the blow-up time by using the differential inequality technique. It is mentioned that the blowing up of solutions to nonlinear PDEs is usually defined in the L∞L∞-norms, while the lower bounds of blow-up time are all determined via some measures in the form of energy integrals. So, in general, to estimate the lower bounds of blow-up time, it has to be assumed that the solutions do blow up in finite time with the involved integral measure before establishing their lower bounds of blow-up time. Such assumptions are unnecessary in this paper.

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Physical Sciences and Engineering Mathematics Applied Mathematics
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