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

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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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Correspondence to Lu Yang.

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

Communicated by Y. Ni.

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

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  • Damped nonlinear wave equations
  • Logarithmic nonlinearity
  • Global existence
  • Asymptotic behavior