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Volume 16, Issue 3
The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H

Yueling Jia

J. Part. Diff. Eq., 16 (2003), pp. 275-288.

Published online: 2003-08

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  • 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.
  • Keywords

generalized Korteweg-de Vries-Burgers equation Cauchy problem space-time dual estimates \dot{H}^{-s} solution

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@Article{JPDE-16-275, author = {Yueling Jia }, 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/}, url = {http://global-sci.org/intro/article_detail/jpde/5425.html} }
TY - JOUR T1 - The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H AU - Yueling Jia 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.
Yueling Jia . (2003). The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H. Journal of Partial Differential Equations. 16 (3). 275-288. doi:
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