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November  2009, 24(4): 1293-1306. doi: 10.3934/dcds.2009.24.1293

Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems

1. 

Department of Applied Mathematics, Donghua University, Shanghai 200051, China

2. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received  August 2008 Revised  February 2009 Published  May 2009

In this paper, we study an initial-boundary value problem for a semilinear hyperbolic system with the initial date having a possibly continuous oscillatory spectrum in the half-space $R^{1+2}_+=\{x=(t,y_{1},y_{2}):t>0,y_{2}>0\}. $ The goal of this paper is to rigorously justify the asymptotic analysis for the reflection of wave trains with such a continuous oscillatory spectrum.
Citation: Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293
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