Initial boundary value problem for fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity

Peng Shi; Min Jiang; Fugeng Zeng; Yao Huang; Peng Shi; Min Jiang; Fugeng Zeng; Yao Huang

doi:10.3934/mbe.2021144

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2832-2848. doi: 10.3934/mbe.2021144

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Initial boundary value problem for fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity

School of Date Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Received: 16 February 2021 Accepted: 15 March 2021 Published: 24 March 2021

In this paper, we study the initial boundary value problem for a class of fractional $ p $-Laplacian Kirchhoff type diffusion equations with logarithmic nonlinearity. Under suitable assumptions, we obtain the extinction property and accurate decay estimates of solutions by virtue of the logarithmic Sobolev inequality. Moreover, we discuss the blow-up property and global boundedness of solutions.
- Kirchhoff type,
- $ p $-Laplacian,
- fractional,
- extinction,
- decay estimate
Citation: Peng Shi, Min Jiang, Fugeng Zeng, Yao Huang. Initial boundary value problem for fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2832-2848. doi: 10.3934/mbe.2021144

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Abstract

In this paper, we study the initial boundary value problem for a class of fractional $ p $-Laplacian Kirchhoff type diffusion equations with logarithmic nonlinearity. Under suitable assumptions, we obtain the extinction property and accurate decay estimates of solutions by virtue of the logarithmic Sobolev inequality. Moreover, we discuss the blow-up property and global boundedness of solutions.

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