O zobecnění modelu nelineární odezvové funkce okolního prostředí Pasternakova typu

Abstract eng:
Mathematical model of special pseudointeractive set consisting of free elastic body and two-parametrical bilateral or unilateral subsoil of Pasternak’s type has been introduced. Sketch of the mathematical apparatus used for formulation and solvability proof of the semi-coercive non-linear boundary-value problems has been given. Idea of the statement proof is illustrated: decomposition of Sobolev function space into a cone of rigid displacement with zero deformation energy and its negative polar cone has been used to prove the existence of the solution. Attention has been focused on the semi-coercive problems representing beam (plate) models on unilateral non-linear subsoil and having kept some degrees of freedom. Solvability condition guaranteeing existence and uniqueness of model problem solution is formulated in the semi-coercive model case. Variants of Pasternak subsoil model, corresponding coercive and semi-coercive problems are illustrated on several model examples.

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