Abdukarimov, M. F.
Published in
Moscow University Mathematics Bulletin

AbstractThe paper studies one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient. The solvability of the problem under consideration is proved. In addition, it is established that the solution to the mixed problem under study is stable with respect to an additive perturbation of the coefficient, as well as with re...

Ergashev, T. G.
Published in
Lobachevskii Journal of Mathematics

AbstractIn earlier research, the double- and simple layer potentials have been successfully applied in solving boundary value problems for two-dimensional elliptic equations. Despite the fact that all fundamental solutions of a three-dimensional elliptic equation with one, two and three singular coefficients were known, the potential theory was not...

Mammadov, Yu. A. Ahmadov, H. I.
Published in
Russian Mathematics

We study a one-dimensional mixed problem for the heat equation, with time advance in nonlocal and non-self-adjoint boundary conditions, describing a real physical process. Under minimal conditions on the initial data, we prove its unique solvability and obtain an explicit representation for the solution.

Aliev, A. B. Shafieva, G. Kh.
Published in
Mathematical Notes

Vishnevskii, M. P. Priimenko, V. I.
Published in
Siberian Mathematical Journal

We consider mixed problems for nonlinear equations of magnetoelasticity. Our main result in the three-dimensional case is the proof of an existence and uniqueness theorem; uniqueness is established under some extra restrictions on the smoothness of solutions. We also manage to prove the existence and uniqueness of a weak solution to the problem in ...

Vishnevskii, M. P. Priimenko, V. I.
Published in
Siberian Mathematical Journal

We consider the direct problems for poroelasticity equations. In the low-frequency approximation we prove existence and uniqueness theorems for the solution to a certain mixed problem. In the high-frequency approximation we establish the uniqueness of a weak solution to the mixed problem and its continuous dependence on the data in the cases of bou...

Mkhitaryan, S. M.
Published in
Mechanics of Solids

In the case of antiplane deformation, a mixed boundary value problem of the nonlinear steady-state creep theory (NSSCT) is considered for the power law of relation between stresses and strain rates for a half-space, when the strain rates are set on one part of its boundary plane while the tangential stresses are equal to zero on the other part of i...

Berkovich, V. N. Builo, S. I.
Published in
Russian Journal of Nondestructive Testing

We consider the problem in the dynamic theory of elasticity about steady-state oscillations in a massive elastic body that is at the pre-fracture stage of material under antiplane strain. The process of acoustic emission (AE) at the stage of accumulation of defects representing a finite tree graph directed toward the free boundary of the elastic bo...

Burlutskaya, M. Sh.
Published in
Computational Mathematics and Mathematical Physics

AbstractA mixed problem for a first-order differential system with two independent variables and a continuous potential, the corresponding spectral problem for which is the Dirac system, is studied. Using a special transformation of the formal solution and refined asymptotics of the eigenfunctions, the classical solution of the problem is obtained....

Skubachevskii, A. L. Tsuzuki, Y.
Published in
Computational Mathematics and Mathematical Physics

We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently ...