On existence of solution for a class of semilinear elliptic equations with nonlinearities that lies between different powers.
On existence of solutions for the nonstationary Stokes system with boundary slip conditions
Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to , and pressure belongs to for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing...
On existence of the weak solution for nonlinear diffusion equation
The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.
On existence of the weak solution for non-linear partial differential equations of elliptic type
On existence of the weak solution for non-linear partial differential equations of elliptic type. II.
On explicit and numerical solvability of parabolic initial-boundary value problems.
On exponential convergence to a stationary measure for a class of random dynamical systems
For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.
On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
On exponentially bounded solutions of linear parabolic difference-differential equations
On extensions of the Mittag-Leffler theorem
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
On extrema of functionals
On -differentiable Fredholm operators of nonstationary initial-boundary value problems
We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.
On factorization and partial indices of unitary matrix-functions of one class.
On factorization of Fefferman's inequality
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...
On FEM solution for 3D continuous casting problem
On Fenchel dual schemes in convex optimal control problems
On finite difference schemes of high order accuracy for elliptic equations with mixed derivatives
On finite element approximation of flow induced vibration of elastic structure
In this paper the fluid-structure interaction problem is studied on a simplified model of the human vocal fold. The problem is mathematically described and the arbitrary Lagrangian-Eulerian method is applied in order to treat the time dependent computational domain. The viscous incompressible fluid flow and linear elasticity models are considered. The fluid flow and the motion of elastic body is approximated with the aid of finite element method. An attention is paid to the applied stabilization...
On Finite Element Approximation of the Gradient for Solution of Poisson Equation.