This article is cited in 1 paper

Differential Equations

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

A. R. Khashimov

Tashkent Financial Institute, Tashkent, Uzbekistan

Abstract: In the paper the second boundary value problem for the third order composite type equations is investigated. We established Saint-Venant's 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.

Keywords: uniqueness theorem, Saint-Venant's principle, third order differential equations, singular points, general solutions, unbounded domains.

UDC: 517.956.6

MSC: Primary 35A02; Secondary 35B40, 35B45, 35D30, 35G15

Original article submitted 09/I/2011
revision submitted – 04/III/2012

DOI: 10.14498/vsgtu912

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