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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1996; 33(3): 557-573

Printed September 1, 1996

Copyright © The Korean Mathematical Society.

On the generalized Korteweg-de Vries equation with dissipation

Youngsoo Choi

Hankuk University of Foreign Studies

Abstract

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The purpose of this work is to study the well-posedness for the initial value problem of the generalized nonlinear-dispersive-dissipative equations. Our method of proof depends heavily on the several mixed-norm estimates using the dissipative character in the associated linear problem and the contraction mapping principle.

Keywords: KdV equations, dispersion and dissipation

MSC numbers: Primary 35Q53, 35J05, 35J10, 35K05, 58F07

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