On solutions representation in factorization method

Abstract

The double factorization method is developed as applied to boundary-value problems for sets of differential equations in partial derivatives of any finite order with constant factors. The study is carried out in arbitrary convex domains with a smooth boundary. Application of the factorization method makes it possible to write out its solution representation, to study quantitative properties of the solutions, and to use different strategies while formulating boundary-value problems irrespective of the fact whether the resolvability of the problem has been proved a priori. The latter is the advantage of factorization method compared with numerical methods. Unlike methods of boundary and finite elements, a method of fundamental solutions, differential methods, the factorization method makes it possible to identify multivariate multi-parameter singular and bifurcation multitudes of boundary-value problems when the problem is a result of linearization of nonlinear problems in seismology.