Asymptotic Expansions of Solutions of InitialBoundary Value Problems for a Dispersive Hyperbolic Equation Classic Reprint
Idioma: inglés
Editorial: Forgotten Books, 2018
- Tapa blanda
- Nuevo
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Vendedor de IberLibro desde 11 de junio de 1999
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N° de ref. del artículo LW-9780366771547
- Título
- Asymptotic Expansions of Solutions of InitialBoundary Value Problems for a Dispersive Hyperbolic Equation Classic Reprint
- Autor
- Norman Bleistein
- Editorial
- Forgotten Books
- Año de publicación
- 2018
- Estado
- New
- Encuadernación
- PAP
- Idioma
- inglés
- ISBN 10
- 036677154X
- ISBN 13
- 9780366771547
- Peso del artículo
- 129 gramos
Recently, the ray method has been applied to time dependent problems and in particular, dispersive hyperbolic equations A particular equation of this type, the klein-gordon equation, may be used to describe the propagation of electromagnetic waves in certain plasmas Initial-boundary value problems for this equation are presently being studied, since it is the simplest example of a large class of dispersive hyperbolic equations.
As of now, there is no general proof that the ray method actually yields the asymptotic expansion of the exact solution. The purpose of the research in this paper is to compare the leading term of the asymptotic expansion of the exact solution and the ray solution for particular problems. The results are shown to agree and thereby add to the overwhelming evidence that the ray method is valid.
We consider initial - boundary value problems in two space dimensions for the klein-gordon equation. The boundary is a parabola and.we require that the solution satisfy a homogeneous condition.
The total solution is assumed to consist of a sum of a primary field and a reflected field. The associated rays are called primary and reflected rays and are straight lines in space time. The primary field must satisfy the equation and the initial conditions. The reflected field is taken to be zero initially and is determined at the boundary in such a way that the total solution satisfies the given boundary condition. The primary rays are emitted from the plane t O in space-time. For each primary ray incident on the boundary, a reflected ray is produced.
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