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Decay of the energy for the Benjamin–Bona–Mahony equation posed on bounded intervals and on a half‐line
Author(s) -
Larkin Nikolai A.,
Vishnevskii Mikhail P.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1594
Subject(s) - bounded function , mathematics , half line , dissipative system , uniqueness , infinity , mathematical analysis , convergence (economics) , initial value problem , line (geometry) , boundary value problem , nonlinear system , real line , physics , geometry , quantum mechanics , economics , economic growth
This paper concerns nonlinear dissipative initial boundary value problems for the Benjamin–Bona–Mahony equation posed on a half‐line and on bounded intervals. We prove the existence and uniqueness of global solutions and decay of the energy as time tends to infinity as well as convergence of solutions on bounded intervals to a solution on a half‐line. Copyright © 2012 John Wiley & Sons, Ltd.