Some Problems of Linear Thermoelasticity in the Ginzburg–Landau Theory of Phase Transitions

The well-posedness of the problem of linear thermoelasticity in the Ginzburg–Landau theory of phase transitions is proved.     

Modeling of the hydrodynamics of a facility for removing mechanical impurities from oil

The separation of a viscous fluid flow by means of a device operating on the centrifugal principle was modeled. Parameters of the device with a specified separation size were obtained in a series of numerical experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 108–112, July–August, 2008.     

The third boundary value problem for the system of equations of linear thermoelasticity

The existence and uniqueness of a generalized solution are proved for the third boundary value problem for a system of differential equations in the linear thermoelasticity theory. The displacement vector and temperature of the medium are the sought functions. The existence of a solution is proved, using the contraction mapping principle. In obtaining some necessary a priori estimates, the expansion of the solution was used in a series of generalized eigenfunctions of the Laplace operator.     

On the Question of Existence of a Solution to the Tricomi Problem for One Class of Systems of Mixed-Type Equations

We establish extremal properties of regular and weak solutions to the Tricomi problem for a system of mixed-type equations. Using a Schwartz-type alternation method, we prove unique weak solvability of the Tricomi problem under some constraints on coefficients.