### AIMS Mathematics

2021, Issue 2: 1209-1222. doi: 10.3934/math.2021074
Research article

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

• 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.

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

### Related Papers:

• 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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