On a boundary value problem with shift for an equation of mixed type in an unbounded domain

We study the unique solvability of a problem with shift for an equation of mixed type in an unbounded domain. We prove the uniqueness theorem under inequality-type constraints for known functions for various orders of the fractional differentiation operators in the boundary condition. The existence of a solution is proved by reduction to a Fredholm equation of the second kind, whose unconditional solvability follows from the uniqueness of the solution of the problem.     

A boundary value problem for a class of mixed-type equations in an unbounded domain

We consider a boundary value problem for an equation of the mixed type with a singular coefficient in an unbounded domain. The uniqueness of the solution of the problem is proved with the use of the extremum principle. In the proof of the existence of a solution of the problem, we use the method of integral equations.     

First boundary-value problem for a class of integrodifferential equations

Lithuanian Mathematical Journal -     

A boundary-value problem in an unbounded strip

Using the generalized scheme of the method of separation of variables we propose a new approach to the study of a boundary-value problem in an unbounded strip for hyperbolic partial differential equations of even order with respect to time. In the space of entire functions of exponential type (with respect to the spatial variable) we single out a unique solution class for the problem and exhibit an algorithm for constructing a solution of it. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 16–21.     

On the Neumann problem for higher-order divergent elliptic equations in an unbounded domain,close to a cylinder

The Neumann problem for a higher-order divergent elliptic equation, defined in an unbounded domain, close to a cylinder, is investigated. It is proved that each solution, having a slowly increasing energy integral, tends at infinity to a certain polynomial and, in the case of an exponential decrease of the righthand side of the equation, the convergence rate is also exponential. Existence and uniqueness are obtained in classes of functions with bounded or unbounded energy integral. Formulas, expressing the coefficients of the limit polynomial in terms of the right-hand side of the equation and of the Dirichlet data at the base of an unbounded domain, close to a semiinfinite cylinder, are derived.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 191–217, 1992.     

Existence and uniqueness of the solution to a free boundary-value problem with thermocapillary convection in an unbounded domain

A free boundary-value problem for a nonisothermal flow of two heavy viscous incompressible capillary liquids descibing a slot coating process is mathematically studied. The problem is stationary and two-dimensional and the Boussinesq approximation for the Navier-Stokes equations is used. The existence and uniqueness of a weak solution is proved in weighted Holder spaces for small data.     

On the behavior of large values of the time required for solving the second boundary-value problem for the Barenblatt-Zheltov-Kochina equation in an unbounded domain

Mathematical Notes -     

On the two-point boundary-value problem for equations of geodesics

For equations of “geodesic spray” type with continuous coefficients on a complete Riemannian manifold, some interrelations between certain geometric characteristics, the distance between points, and the norm of the right-hand side that guarantee the solvability of the boundary-value problem are found. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 65–70, 2005.     

Attractors for generalized Ginzburg-Landau-BBM equations in an unbounded domain

By the interpolation inequality and a priori estimates in the weighted space, the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained. This research is supported by the National Natural Science Foundation of China (No.19861004).     

On an initial boundary-value problem for a model system of equations of a granulated medium

In this paper we consider an initial boundary-value problem for the system of equations describing the motion of a granulated medium with constant density. We introduce the notion of a weak solution of the problem and prove the existence of such a solution.     

Mixed problem for a semilinear ultraparabolic equation in an unbounded domain

We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation {fx1870-01} in an unbounded domain with respect to the variables x. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1661–1673, December, 2007.     

The boundary-value problem for degenerate ultraparabolic equations of the Sobolev type

In this paper we study the first boundary-value problem for a class of degenerate equations of the Sobolev type and prove existence and uniqueness theorems for regular solutions to the considered problem.     

Dirichlet problem for a divergence form elliptic equation with unbounded coefficients in an unbounded domain

We prove existence and uniqueness of the solution of the Dirichlet problem for a class of elliptic equations in divergence form with discontinuous and unbounded coefficients in unbounded domains. Entrata in Redazione il 22 aprile 1999.