GLOBAL C1 SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LINEARLY DEGENERATE CHARACTERISTICS

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Initial-boundary value problem global C1 solution quasilinear hyperbolic system of diagonal form linearly degenerate characteristics.
• 年，卷（期）: 2003,（1）
• 页码范围: 8-17
• 页数: 10页
• 分类号: O175.22.
• 语种: 英文

摘要

Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.