Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity

Famei Zheng; Famei Zheng

doi:10.3934/math.2021074

AIMS Mathematics

2021, Volume 6, Issue 2: 1209-1222. doi: 10.3934/math.2021074

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Research article

Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity

Famei Zheng ^,

School of Mathematics and Statistics, Huaiyin Normal University, Huaian Jiangsu, 223300 P. R. China

Received: 04 September 2020 Accepted: 26 October 2020 Published: 12 November 2020
MSC : 34C37, 35C07

This paper is concerned with the existence of periodic wave solutions for a type of non-Newtonian filtration equations with an indefinite singularity. A sufficient criterion for the existence of periodic wave solutions for non-Newtonian filtration equation is provided via an innovative method of combining a new continuation theorem with coincidence degree theory as well as mathematical analysis skills. The novelty of the present paper is that it is the first time to discuss the existence of periodic wave solutions for the indefinite singular non-Newtonian filtration equations. Finally, two numerical examples are presented to illustrate the effectiveness and feasibility of the proposed criterion in the present paper.
- periodic wave solution,
- singularity,
- continuation theorem,
- existence
Citation: Famei Zheng. Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity[J]. AIMS Mathematics, 2021, 6(2): 1209-1222. doi: 10.3934/math.2021074

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Abstract

This paper is concerned with the existence of periodic wave solutions for a type of non-Newtonian filtration equations with an indefinite singularity. A sufficient criterion for the existence of periodic wave solutions for non-Newtonian filtration equation is provided via an innovative method of combining a new continuation theorem with coincidence degree theory as well as mathematical analysis skills. The novelty of the present paper is that it is the first time to discuss the existence of periodic wave solutions for the indefinite singular non-Newtonian filtration equations. Finally, two numerical examples are presented to illustrate the effectiveness and feasibility of the proposed criterion in the present paper.

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