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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
##### Keywords:
averaging theorem; locally non-resonant curves
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##### References:
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