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Well-Posedness of Solutions for the Sixth-Order Boussinesq Equation with Linear Strong Damping and Nonlinear Source

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Abstract

The object of this paper is to study a sixth-order Boussinesq equation with dispersive, linear strong damping and nonlinear source by using potential well methods, including the following aspects: firstly, the local well-posedness of the solutions is studied; secondly, the global existence and the finite time blow-up conditions are studied at two different initial energy levels by using the relationship between the initial energy and the depth of the potential well; thirdly, a blow-up condition independent of the depth of the potential well is established and by using of this condition, the existence of blow-up solutions at arbitrary initial energy level is studied; finally, the upper bound estimation of blow-up time and some necessary and sufficient conditions for existing finite time blow-up solutions are established.

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jun Zhou & Huan Zhang

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  1. Jun Zhou
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Zhou, J., Zhang, H. Well-Posedness of Solutions for the Sixth-Order Boussinesq Equation with Linear Strong Damping and Nonlinear Source . J Nonlinear Sci 31, 76 (2021). https://doi.org/10.1007/s00332-021-09730-4

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