THE CAUCHY PROBLEM FOR THE GENERALIZED KORTEWEG-DE VRIES-BURGERS EQUATION IN H-s

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: generalized Korteweg-de Vries-Burgers equation Cauchy problem space-time dual estimates H-s solution.
• 年，卷（期）: 2003,（3）
• 页码范围: 275-288
• 页数: 14页
• 分类号: O175.28,O175.29
• 语种: 英文

摘要

The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in Lq (0, T; Lp)∩ L∞(0, T; H-s)(0 ≤ s ＜ 1) are obtained for initial data inH-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.