Asymptotic properties of singular solutions in degenerate parabolic equation with boundary flux

ABSTRACT

This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively.

KEYWORDS:

• Degenerate parabolic equation
• blow-up rate
• quenching rate
• blow-up set
• quenching set

MSC (2010):

• 35K55
• 35B40
• 35K15
• 35B33

Acknowledgments

The authors would like to thank the anonymous Referees and the Editors for valuable and constructive suggestions improving the first version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is supported by Shandong Provincial Natural Science Foundation, China (ZR2016AM12, ZR2017LA003).