1 - 10 of 11 articles
A first-order regularized trace formula has been obtained for the Sturm–Liouville operatorwith a point of...
We obtain sufficient as well as necessary and sufficient conditions for linearone-dimensional homogeneous stochastic differential equations with independent standard andfractional Brownian motions to possess some types of stability.
Various tests for the exponential stability of a linear system of ordinary differentialequations are obtained by the method of frozen coefficients. To this end, we prove and usean improved Gelfand–Shilov estimate for the matrix exponential. The cases in which thecoefficient matrix of the system...
We consider biquaternionic wave (biwave) equations. They are biquaternionicgeneralizations of the Maxwell and Dirac equations and are equivalent to a system of eightdifferential equations of hyperbolic type. Using the theory of generalized functions, we constructfundamental and generalized...
We consider the first initial–boundary value problem for a spatially one-dimensionalsecond-order Petrovskii parabolic system with differentiable coefficients in a half-strip withnonsmooth lateral boundary. A theorem on the uniqueness of the classical solution of this problemis proved.
The global solvability of boundary value problems for the reaction–diffusion–convectionequation is proved for the case in which the reaction coefficient in the equation and the masstransfer coefficient in the boundary condition nonlinearly depend on the substance concentration.The minimum and...
We consider unsteady triaxial tension–compression of a moving parallelepiped filled with aNewtonian viscous fluid and changing its linear dimensions (with a constant volume) duringmotion. The statement of the linearized problem is given in terms of three-dimensionalperturbations imposed on the...
We consider a boundary value problem for an elliptic differential equation with analyticcoefficients that is degenerate in one of the variables in a rectangle. Using the method of spectralseparation of singularities, a solution of this problem is constructed in the form of a Poissonseries—a...
Green’s functions for the Navier and Riquier–Neumann problems for the biharmonicequation in the unit ball are constructed, and integral representations of the solution of theseproblems are given.
We consider the analytic continuation problem for the solution of the system ofthermoelasticity equations in a spatial domain based on its values and the values of its stressesknown on part of the domain boundary, i.e., the Cauchy problem.
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