Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

нелинейные системы уравнений с частными производными

Configuration Space in Second Boundary Value Problem of Non-classical Plate Theory

The article contains investigation of second boundary value problem for equilibrium equation «in mixed formulation» describing nonclassical mathematical model for hinged isotropic and uniform plate under generalized Timoshenko hypothesis taking into account initial irregularities. For this problem for the first time were proved the existance of generalized solution and weak compactness of the set of approximate solutions obtained with Bubnov–Galerkin method using V. Z. Vlasov scheme.

Solvability of Evolutionary Equations in Generalized Transmission Problems for Shallow Shells

We prove the solvability of the generalized transmission problem in the non-classical theory of shallow shells using the method of compactness and a new way of obtaining a priori estimates.