Long‐time asymptotics of solutions of the second initial‐boundary value problem for the damped Boussinesq equation

Vladimir V. Varlamov

Abstract and Applied Analysis, 1997, vol. 2, issue 3-4, 281-299

Abstract: For the damped Boussinesq equation utt−200butxx=−αuxxxx+uxx+β(u2)xx,x∈(0,π),t>;α,b=const>,β=const∈R1, the second initial‐boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long‐time asymptotics is obtained in the explicit form and the question of the blow up of the solution in a certain case is examined. The possibility of passing to the limit b → +0 in the constructed solution is investigated.

Date: 1997
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https://doi.org/10.1155/S1085337597000407

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2:y:1997:i:3-4:p:281-299

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