Geodesic
On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 18-25

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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, third order differential equations, singular points, general solutions, unbounded domains.
Mots-clés : Saint-Venant's principle 
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     author = {A. R. Khashimov},
     title = {On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {18--25},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a1/}
}
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A. R. Khashimov. On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 18-25. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a1/