@Article{JPDE-16-3,
author = {},
title = {The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H},
journal = {Journal of Partial Differential Equations},
year = {2003},
volume = {16},
number = {3},
pages = {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.},
issn = {2079-732X},
doi = {https://doi.org/2003-JPDE-5425},
url = {https://global-sci.com/article/88592/the-cauchy-problem-for-the-generalized-korteweg-de-vries-burgers-equation-in-h}
}