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Coupled system of Korteweg‐de Vries equation‐type in domains with oscillatory moving boundaries
Author(s) -
Vera Octavio,
Sepúlveda Mauricio,
Bisognin Vanilde
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700587
Subject(s) - korteweg–de vries equation , uniqueness , bounded function , type (biology) , domain (mathematical analysis) , mathematics , mathematical analysis , boundary value problem , boundary (topology) , physics , nonlinear system , geology , quantum mechanics , paleontology
We consider the initial‐boundary value problem in a bounded domain with oscillatory moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of KdV type modelling strong interactions between internal solitary waves. We give a result of global existence and uniqueness for strong solutions for the coupled system of equations of Korteweg – de Vries type as well as the exponential decay of small solutions in asymptotically cylindrical domains. We present a numerical examples based in semi‐implicit finite differences showing the numerical effect of the oscillatory moving boundaries for this kind of systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)