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, 1-19

Abstract:

For the damped Boussinesq equation u t t − 2 b u t x x = − α u x x x x + u x x + β ( u 2 ) x x , x ∈ ( 0 , π ) , t > 0 ; α , b = c o n s t > 0 , β = c o n s t ∈ R 1 , 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:913705

DOI: 10.1155/S1085337597000407

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