Comparison of exact and approximate causal solutions of a model curved- space wave equation. (English) Zbl 0632.35032
A retarded Green function is constructed for a model curved space-time scalar wave equation and used to find the solution to the equation for a pure-frequency point source. This solution is shown to be unique and causal. It is then given an asymptotic expansion in a small parameter and compared with the result obtained by applying singular perturbation methods to the same problem. The aim is to show that such perturbative solutions are asymptotic to exact solutions.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 35B20 | Perturbations in context of PDEs |
| 35A35 | Theoretical approximation in context of PDEs |
| 35C20 | Asymptotic expansions of solutions to PDEs |
Keywords:
retarded Green function; curved space-time; pure-frequency point source; asymptotic expansion; small parameter; singular perturbationReferences:
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