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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 7
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Articles

The uniqueness of the solution to the diffusion equation with a damping term

Pages 1333-1346 | Received 27 Apr 2017, Accepted 23 Dec 2017, Published online: 08 Jan 2018
 

ABSTRACT

Consider a non-linear diffusion equation with a damping term. If the diffusion coefficient is positive, then the solutions are not unique generally. However, if the diffusion coefficient degenerates, the situation may change. In this paper, not only the existence of the weak solution is established, but also the uniqueness of the weak solutions is proved, even the boundary value condition is not imposed. The conclusions imply that, on the boundary, the degeneracy of diffusion coefficient can eliminate the action from the damping term.

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Acknowledgements

I would like to express my very sincerely thanks to the reviewers for their valuable amendments.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The paper is supported by Natural Science Foundation of Fujian province [grant number 2015J01592], supported by Science Foundation of Xiamen University of Technology, China.

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