Decay estimate and non-extinction of solutions of p-Laplacian nonlocal heat equations

Sarra Toualbia; Abderrahmane Zaraï; Salah Boulaaras; Sarra Toualbia; Abderrahmane Zaraï; Salah Boulaaras

doi:10.3934/math.2020112

AIMS Mathematics

2020, Volume 5, Issue 3: 1663-1679. doi: 10.3934/math.2020112

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Research article

Decay estimate and non-extinction of solutions of p-Laplacian nonlocal heat equations

1.
Laboratory of mathematics, Informatics and Systems (LAMIS), department of Mathematics and Computer Science, Larbi Tebessi University, 12002 Tebessa, Algeria
2.
Department of Mathematics, College of Sciences and Arts, Al-Rass, Qassim University, Buraydah, Kingdom of Saudi Arabia
3.
Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Algeria

Received: 04 October 2019 Accepted: 20 January 2020 Published: 11 February 2020
MSC : 35A01, 35K55, 35B44

The main goal of this work is to study the initial boundary value problem of a nonlocal heat equations with logarithmic nonlinearity in a bounded domain. By using the logarithmic Sobolev inequality and potential wells method, we obtain the decay, blow-up and non-extinction of solutions under some conditions, and the results extend the results of a recent paper Lijun Yan and Zuodong Yang (2018).
- global existence,
- decay estimates,
- potential well,
- blow-up,
- non-extinction,
- nonlocal heat equations
Citation: Sarra Toualbia, Abderrahmane Zaraï, Salah Boulaaras. Decay estimate and non-extinction of solutions of p-Laplacian nonlocal heat equations[J]. AIMS Mathematics, 2020, 5(3): 1663-1679. doi: 10.3934/math.2020112

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Abstract

The main goal of this work is to study the initial boundary value problem of a nonlocal heat equations with logarithmic nonlinearity in a bounded domain. By using the logarithmic Sobolev inequality and potential wells method, we obtain the decay, blow-up and non-extinction of solutions under some conditions, and the results extend the results of a recent paper Lijun Yan and Zuodong Yang (2018).

References

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