We prove a priori estimates for a solution of the first initial boundary-value problem for a system of fully nonlinear partial differential equations (PDE) in a bounded domain. In the proof, we reduce the initial boundary-value ...

The purpose of this paper is to investigate an operator version of Tikhonov regularization for a class of ill-posed variational inequalities under arbitrary perturbation operators. Aspects of convergence rate and ...

We obtain the direct reduction of representations of a dyadic set S such that |Ind C(S)| < ∞ to the bipartite case.

We consider the class of continuous measure-valued processes {μ t } on a finite-dimensional Euclidean space X for which ∫fd μ t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R ...

We consider a quasilinear system of difference equations with certain conditions. We prove that there exists a formal partial o-solution of this system in the form of functional series of special type. We also prove a ...

The Volterra integral equation of the second order with a regular singularity is considered. Under the conditions that a kernel K(x,t) is a real matrix function of order n×n with continuous partial derivatives up to order ...

In 1980–1984, V. K. Dzyadyk suggested and modified an iterative approximation method (IA-method) for numerical solution of the Cauchy problem y′=f(x,y), y(x₀)=x₀. Particular cases of nonlinear mixed Volterra-Fredholm ...

We consider the transition semigroup Rt =e tsA associated to an Ornstein—Uhlenbeck process in a Hilbert space H. We characterize, under suitable assumptions, the domain of A as a subspace W²,²(H, μ), where μ is the invariant ...

Problems of singular perturbation of reducible invertible operators are classified and their applications to the analysis of stochastic Markov systems represented by random evolutions are considered. The phase merging, ...