METHOD OF ASYMPTOTIC PARTIAL DECOMPOSITION OF DOMAIN

A new method of partial decomposition of a domain is proposed for part ial differential equations, depending on a small parameter. It is base d on the information about the structure of the asymptotic solution in different parts of the domain. The principal idea of the method is to extract the subdomain of singular behavior of the solution and to sim plify the problem in the subdomain of regular behavior of the solution . The special interface conditions are imposed on the common boundary of these partially decomposed subdomains. If, for example, the domain depends an the small parameter and some parts of the domain change the ir dimension after the passage to the limit, then the proposed method reduces the initial problem to the system of equations posed in the do mains of different dimensions with the special interface conditions.