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

• 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.
Mathematics Subject Classification: 28B05, 35B05, 35L60, 35Q60.

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