Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-15

Journal: APPLIED MATHEMATICS AND COMPUTATION

Included Journals: Scopus、EI、SCIE

Volume: 251

Page Number: 331-335

ISSN: 0096-3003

Key Words: Degenerate diffusion equation; Blow-up time; Gradient absorption

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-infinity-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-infinity-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. (C) 2014 Elsevier Inc. All rights reserved.