Oscillatory asymptotic expansion for semilinear wave equation (Q2747390)
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scientific article; zbMATH DE number 1657645
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Oscillatory asymptotic expansion for semilinear wave equation |
scientific article; zbMATH DE number 1657645 |
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Oscillatory asymptotic expansion for semilinear wave equation (English)
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5 May 2002
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oscillatory terms in initial data
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energy type estimates for transport equation
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We study oscillatory properties of the solution to a semilinear wave equation, assuming the oscillatory terms in the initial data have sufficiently small amplitude. The main result gives an a priori estimate of the remainder in the approximation by means of the method of geometric optics. The method of establishing this estimate is based on a combination between energy type estimates for transport equation and Sobolev embedding.
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