Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation. (1997)

• Record Type: Journal Article
• Authors: Varlamov, Vladimir V.
• Is Part Of: Abstract and applied analysis. Volume 2:Number 3/4(1997)
• Page Start: 281
• Page End: 299
• Publication Date: 1997
• Subjects: Boussinesq equation -- initial-boundary value problem -- long-time asymptotics; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337597000407
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : For the damped Boussinesq equationu 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 limitb → + 0 in the constructed solution is investigated.