ASYMPTOTIC BEHAVIOR OF GLOBAL CLASSICAL SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Quasilinear hyperbolic system Global classical solution Asymptotic behavior Weak linear degeneracy Normalized coordinates Travelling wave
• 年，卷（期）: 2007,（2）
• 页码范围: 114-130
• 页数: 17页
• 分类号: O175.22|O175.27
• 语种: 英文

摘要

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity,the solution approaches a combination of C1 travelling wave solutions at the algebraic rate (1 + t)-μ, provided that the initial data decay at the rate (1 + x)-(1+μ) as x tends to +∞ and the boundary data decay at the rate (1 + t)-(1+μ) as t tends to +∞, where μ is a positive constant.