Volume 18, Issue 2
Long-time Asymptotic for the Damped Boussinesq Equation in a Circle

Yi Zhang , Qun Lin & Shaoyong Lai

J. Part. Diff. Eq., 18 (2005), pp. 97-113.

Published online: 2005-05

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  • 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.

  • Keywords

Damped Boussinesq equation initial-boundary value problem long-time asymptotics

  • AMS Subject Headings

35K55.

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COPYRIGHT: © Global Science Press

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@Article{JPDE-18-97, author = {}, title = {Long-time Asymptotic for the Damped Boussinesq Equation in a Circle}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {2}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5347.html} }
TY - JOUR T1 - Long-time Asymptotic for the Damped Boussinesq Equation in a Circle JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 113 PY - 2005 DA - 2005/05 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5347.html KW - Damped Boussinesq equation KW - initial-boundary value problem KW - long-time asymptotics AB -

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.

Yi Zhang , Qun Lin & Shaoyong Lai . (2019). Long-time Asymptotic for the Damped Boussinesq Equation in a Circle. Journal of Partial Differential Equations. 18 (2). 97-113. doi:
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