Asymptotic expansion of the electromagnetic field in the vicinity of domain’s borders

Abstract

The problem of construction the asymptotic expansion of an electromagnetic field in a vicinity of domainpsilas borders is considered. The solution of a problem is constructed as product of functions so that boundary conditions have been satisfied. In case of zero boundary conditions one of factors in the solution tends to zero on border and consequently near the border can be accepted as small parameter. The Helmholtz equation becomes singularly perturbed and it allows constructing the solution as a boundary layer. The asymptotic expansion is obtained in an explicit form for domains which borders consist on the various combinations of curves of a special kind. It is shown, that asymptotic expansion of the solution is continuous in all a boundary layer.