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Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity

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Abstract

The initial boundary value problem for the nonlinear wave equations with damping and logarithmic nonlinearity is investigated in this paper. By making use of modified potential well theory and the technique of Logarithmic-Sobolev inequality, we establish global existence as well as asymptotic behavior of solution, under the assumption that the initial energy is small. Moreover, we obtain an exponential decay which is much faster than the decay in polynomial nonlinear case of Gazzola and Squassina (Ann I H Poincaré AN 23:185–207, 2006). These results generalize and extend work in application of potential well theory to wave equations.

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Funding

This study was funded by China NSF Grant No. 11601404, Yanta Scholar Fund of Xi’an University of Finance and Economics.

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Authors and Affiliations

  1. Department of Statistics, Xi’an University of Finance and Economics, Xi’an, 710100, China

    Lu Yang & Wei Gao

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  1. Lu Yang
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  2. Wei Gao
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Correspondence to Lu Yang.

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This article does not contain any studies with human participants performed by any of the authors.

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Communicated by Y. Ni.

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Supported in part by China NSF Grant No. 11601404, Yanta Scholar Fund of Xi’an University of Finance and Economics.

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Yang, L., Gao, W. Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity. Soft Comput 24, 2873–2885 (2020). https://doi.org/10.1007/s00500-019-04660-6

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