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Global Existence and Finite Time Blow-up for the m-Laplacian Parabolic Problem

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Abstract

In this paper, we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models. We tackle this problem at three different initial energy levels. For the sub-critical initial energy, we obtain the blow-up result and estimate the lower and upper bounds of the blow-up time. For the critical initial energy, we show the global existence, asymptotic behavior, finite time blow-up and the lower bound of the blow-up time. For the sup-critical initial energy, we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P. R. China

    Yue Pang & Run Zhang Xu

  2. Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059, Kraków, Poland

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585, Craiova, Romania

    Vicenţiu D. Rădulescu

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  1. Yue Pang
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  2. Vicenţiu D. Rădulescu
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  3. Run Zhang Xu
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Correspondence to Run Zhang Xu.

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Supported by the National Natural Science Foundation of China (Grant No. 12271122), the China Postdoctoral Science Foundation (Grant No. 2013M540270), the Fundamental Research Funds for the Central Universities

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Pang, Y., Rădulescu, V.D. & Xu, R.Z. Global Existence and Finite Time Blow-up for the m-Laplacian Parabolic Problem. Acta. Math. Sin.-English Ser. 39, 1497–1524 (2023). https://doi.org/10.1007/s10114-023-1619-7

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  • DOI: https://doi.org/10.1007/s10114-023-1619-7

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