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Large-time asymptotic behaviour of a step for the Benjamin–Bona–Mahony–Burgers equation

Published online by Cambridge University Press:  14 November 2011

P. I. Naumkin
P. I. Naumkin
Affiliation:
Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow 119 899, Russia
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Abstract

The asymptotic behaviour for large-time values of solutions of the initial-boundary-value problem for the Benjamin–Bona–Mahony–Burgers (BBMB) equation is studied. The solution of the initial-boundary-value problem is proved to converge to the standing wave as t → ∞ uniformly with respect to x ∈ R1. The estimate obtained of the time-decay rate of the remainder appears to depend on the rate of decay at infinity of the deviation of initial data from the standing wave. Due to the known expansion formulae with respect to the eigenfunctions associated to the stationary Schrodinger operator with the standing wave as a potential, it is possible to find the second term of the large-time asymptotic expansion of the solution to the initial-boundary-value problem for the BBMB equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 1 - 18
Copyright
Copyright © Royal Society of Edinburgh 1996

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