On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains

Abstract

In the paper the second boundary value problem for the third order composite type equations is investigated. We established Saint-Venants type energy estimates for weak solutions of the problem on Sobolev classes. The obtained estimates are used to prove uniqueness theorems in the classes of functions growing at infinity. These uniqueness classes depend on the geometrical characteristics of the domain. Moreover, energy estimates allowing us to investigate behavior of solution in the neighborhood of singular points were obtained.

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