Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
zbMATH Open document ID: 0919.35111
DOI: 10.1155/S016117129922131X
author: V. V. Varlamov
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-09-02T00:00:00Z
full work available at URL: https://eudml.org/doc/48202
review text: Summary: The Cauchy problem for the damped Boussinesq equation \[ u_{tt}=-\alpha u_{xxxx}+ u_{xx}+ \beta(u^2)_{xx},\quad x\in\mathbb{R}^1,\quad t>0, \] with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 1275566
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: long-time asymptotics
MaRDI profile type: Publication
OpenAlex ID: W2057796566
description: scientific article; zbMATH DE number 1275566