The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H

The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H

Year:    2003

Journal of Partial Differential Equations, Vol. 16 (2003), Iss. 3 : pp. 275–288

Abstract

The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in L^q(0, T;L^p) ∩ L^∞(0, T; \dot{H}^{-s})(0 ≤ s < 1) are obtained for initial data in \dot{H}^{-s}. Moreover, the local solutions are global if the initial data are sufficiently small in critical case. Particularly, for s = 0, the generalized Korteweg-de Vries-Burgers equation satisfies the energy equality, so the initial data can be arbitrarily large to obtain the global solution.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2003-JPDE-5425

Journal of Partial Differential Equations, Vol. 16 (2003), Iss. 3 : pp. 275–288

Published online:    2003-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    generalized Korteweg-de Vries-Burgers equation