boundary problems

Starting Earthquakes with the Parallel Faults of Lithospheric Plates

Authors: Babeshko V. A., Evdokimova O. V., Babeshko O. M., Uafa G. N., Evdokimov V. S.

The analysis of the models characterizing the preparation of starting earthquakes for different types of stresses on tectonic plates enabled to convey the analysis of a possibility of earthquakes for the case of the parallelfaults ,which simultaneously allows to figure ways of the irprediction, i.e.permits to reduce earth quake risk. The investigation of the arisen block structure applied the topological approach. The boundary problem imbeds into the topological structure and transforms in the functional equations.

Boundary Properties of Generalized Cauchy Type Integrals in the Space of Smooth Functions

Authors: Soldatova T. A.

The generalized Cauchy type integrals which kernel depends on the difference of arguments are considered on the smooth contour. These integrals cover as potentials of double layer for second order elliptic equations as generalized Cauchy type integrals for first order elliptic systems on the plane. In the paper the sufficient conditions such that these integrals belong C n,μ up to the boundary are found.

About Completeness of Products of Functions, Initiated by Singular Differential Equations

Authors: Poplavskij D. V.

In this article we introduced the completeness theorem for special vector-functions, initiated by products of Weil solutions of forth order differential equation and its derivatives on the halfline. We prove that such nonlinear combinations of Weil solutions and its derivatives form the linear subspace of solutions, which decrease to infinity, of linear singular Kamke-type differential system.