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Global Solution and Blow-up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity

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Abstract

The main goal of this work is to study an initial boundary value problem for a quasilinear parabolic equation with logarithmic source term. By using the potential well method and a logarithmic Sobolev inequality, we obtain results of existence or nonexistence of global weak solutions. In addition, we also provided sufficient conditions for the large time decay of global weak solutions and for the finite time blow-up of weak solutions.

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Acknowledgements

The authors would like to thank the anonymous referees for their useful comments and suggestions which allowed to improve this paper.

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Authors and Affiliations

  1. Department of Mathematics, An Giang University, Long Xuyen City, Vietnam

    Cong Nhan Le

  2. Faculty of Mathematics and Computer Science, VNUHCM-University of Science, HCM City, Vietnam

    Cong Nhan Le

  3. Department of Mathematics and Statistics, University of Economics Ho Chi Minh City, HCM City, Vietnam

    Xuan Truong Le

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  1. Cong Nhan Le
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  2. Xuan Truong Le
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Correspondence to Xuan Truong Le.

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Le, C.N., Le, X.T. Global Solution and Blow-up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity. Acta Appl Math 151, 149–169 (2017). https://doi.org/10.1007/s10440-017-0106-5

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  • DOI: https://doi.org/10.1007/s10440-017-0106-5

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