Title of article :
APPROXIMATING INITIAL-VALUE PROBLEMS WITH TWO-POINT BOUNDARY-VALUE PROBLEMS: BBM-EQUATION
Author/Authors :
BONA, J. L. University of Illinois at Chicago - Department of Mathematics, Statistics Computer Science, USA , Chen, H. University of Memphis - Department of Mathematical Sciences, USA , Sun, S.M. State University - Virginia Polytechnic Institute - Department of Mathematics, USA , Zhang, B.-Y. University of Cincinnati - Department of Mathematics, USA
Abstract :
The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude, long waves in dispersive media. This evolution equation has been used in both laboratory and field studies of water waves. The principal new result is an exact theory of convergence of the two-point boundary-value problem to the initial-value problem posed on an infinite stretch of the medium of propagation. In addition to their intrinsic interest, our results provide justification for the use of the two-point boundary-value problem in numerical studies of the initial-value problem posed on the entire line.
Keywords :
KdV , equation , BBM , equation , regularized long wave equation
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
