We study magnetohydrodynamic equations for a viscous incompressible resistive fluid in a thin 3D domain. We prove the global existence and uniqueness of solutions corresponding to a large set of initial data from Sobolev type space of the order 1/2 and forcing terms from L2 type space. We also show that the solutions constructed become smoother for positive time and prove the global existence o...

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for d = 2, 3) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity u0 ∈ H (R) for s > 0 in 2-D, or u0 ∈ H (R) satisfying ‖u0‖L2‖∇u0‖L2 being sufficiently small in 3-D. This in particular improves t...

This paper discusses a novel three field formulation for the Darcy-Forchheimer flow with nonlinear viscosity depending on temperature coupled heat equation. We show unique solvability of variational problem by using; Galerkin method, Brouwer’s fixed point and some compactness properties. propose study in detail finite element approximation. A priori error estimate is then derived convergence ob...

We consider a mathematical problem for quasistatic contact between thermo-electro--elastic-viscoplastic body and an obstacle. The is modeled by general normal damped response condition with friction law heat exchange. present variational formulation of the prove existence uniqueness weak solution. proof based on four intermediate problems displacement field, electric potential field temperature...

This paper studies the solvability and stability of a generalized saddle-point system in finiteand infinite-dimensional spaces. Sharp solvability conditions and stability estimates are derived.

Solvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differentia...

We consider discrete-time linear periodic descriptor systems and study the concepts of solvability and conditionability introduced by D. Luenberger. We prove that solvability is equivalent to conditionability, just as in the time-invariant case. We give a characterization of solvability/conditionability in terms of a cyclic matrix pencil and, furthermore, propose a simple test via the periodic ...

<p style='text-indent:20px;'>We consider a Cauchy problem for fractional anisotropic parabolic equation in Hölder spaces. The generalizes the heat to case of power Laplace operator and this can be different with respect groups space variables. time derivative either Caputo - Jrbashyan or usual derivative. Under some necessary conditions on order we show that whole is an isomorphism approp...