Large-time asymptotic behaviour of a step for the Benjamin–Bona–Mahony–Burgers equation
P. I. Naumkin
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Source: Crossref
Published: Jan 1, 1996
DOI: 10.1017/s0308210500030572
Open original source ↗Source 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 ∈ R 1 . 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.
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