TY - JOUR
T1 - The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H
JO - Journal of Partial Differential Equations
VL - 3
SP - 275
EP - 288
PY - 2003
DA - 2003/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5425.html
KW - generalized Korteweg-de Vries-Burgers equation
KW - Cauchy problem
KW - space-time dual estimates
KW - \dot{H}^{-s} solution
AB -  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.