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Blow-up time estimate for a degenerate diffusion equation with gradient absorption

Author

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  • Zhang, Qiuyun
  • Jiang, Zhaoxin
  • Zheng, Sining

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∞-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∞-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.

Suggested Citation

  • Zhang, Qiuyun & Jiang, Zhaoxin & Zheng, Sining, 2015. "Blow-up time estimate for a degenerate diffusion equation with gradient absorption," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 331-335.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:331-335
    DOI: 10.1016/j.amc.2014.11.058
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