Long-time Asymptotic for the Damped Boussinesq Equation in a Circle

Long-time Asymptotic for the Damped Boussinesq Equation in a Circle

Year:    2005

Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 2 : pp. 97–113

Abstract

The first initial-boundary value problem for the following equation u_{tt} - aΔu_{tt} - 2bΔu_t = αΔ^3u - βΔ²u + Δu + ϒΔ(u²) in a unit circle is considered. The existence of strong solution is established in the space C^0([0, ∞), H^s_r (0, 1)), s < 7/2, and the solutions are constructed in the form of series in the small parameter present in the initial conditions. For 5/2 < s < 7/2, the uniqueness is proved. The long-time asymptotics is obtained in the explicit form.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-JPDE-5347

Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 2 : pp. 97–113

Published online:    2005-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Damped Boussinesq equation