Extinction for a p-Laplacian equation with gradient source and nonlinear boundary condition

Abstract

We are concerned with extinction properties for a p-Laplacian equation with gradient source and absorption terms under nonlinear boundary condition. Based on the integral norm estimate method and the technique of differential inequalities, we establish some extinction results and the precise decay estimates of extinction solutions for this problem. Furthermore, we believe that the arguments used in this paper can also be applicable to the problem with nonlocal source instead of a gradient source.

COMMUNICATED BY:

• S. Leonardi

Keywords:

• p-Laplacian equation
• gradient source
• nonlinear boundary condition
• extinction
• decay estimate

2010 Mathematics Subject Classifications:

• 35K67
• 35B40
• 35K61

Acknowledgments

Xianghui Xu is supported by the Natural Science Foundation of Shandong Province of China (ZR2019BA032). The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Xianghui Xu is supported by the Natural Science Foundation of Shandong Province [grant number ZR2019BA032].