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On the weak limit of rapidly oscillating waves. (English) Zbl 0646.73016
A possible representation of a rapidly oscillating wave can be represented as \[ U^{\epsilon}(x,t)=W_ N(\theta (x,t)/\epsilon;\quad \kappa (x,t),\quad \omega (x,t))+O(\epsilon), \] where \(W_ N(\cdot,\kappa,\omega):T^ N\to R\) is defined on the N-torus \(T^ N\) and the N-vectors \(\theta\), \(\kappa\), \(\omega\) are real-valued functions of x and t related by \((\partial \theta /\partial x)=\kappa\), \((\partial \theta /\partial t)=\omega\). An averaging theorem is proved on the so- called locally non-resonant curves \(\kappa:R\to R^ n.\)
Reviewer: V.Rǎsvan

MSC:
74J99 Waves in solid mechanics
35Q99 Partial differential equations of mathematical physics and other areas of application
74J20 Wave scattering in solid mechanics
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