# Vlasenko L. A.

### Optimal control with impulsive component for systems described by implicit parabolic operator differential equations

Samoilenko A. M., Vlasenko L. A.

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1053-1065

We study the problem of optimal control with impulsive component for systems described by abstract Sobolev-type differential equations with unbounded operator coefficients in Hilbert spaces. The operator coefficient of the time derivative may be noninvertible. The main assumption is a restriction imposed on the resolvent of the characteristic operator pencil in a certain right half plane. Applications to Sobolevtype partial differential equations are discussed.

### Problem of impulsive regulator for one dynamical system of the Sobolev type

Rutkas A. G., Samoilenko A. M., Vlasenko L. A.

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1027–1034

We establish conditions for the existence of an optimal impulsive control for an implicit operator differential equation with quadratic cost functional. The results obtained are applied to the filtration problem.

### Forced oscillations of an infinite-dimensional oscillator under impulsive perturbations

Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 155–166

Existence and uniqueness theorems for the impulsive differential operator equation $$ \frac{d^2}{dt^2}[Au(t)] + Bu(t) = f(t, u(t))$$ are obtained. The operator A is allowed to be noninvertible. The results are applied to differential algebraic equations and partial differential equations, which are not equations of Kovalevskaya type.

### On the Solvability of Impulsive Differential-Algebraic Equations

Perestyuk N. A., Vlasenko L. A.

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 458–468

We establish theorems on the existence and uniqueness of a solution of the impulsive differential-algebraic equation $$\frac{d}{{dt}}[Au(t)] + Bu(t) = f(t,u(t)),$$ where the matrix A may be singular. The results are applied to the theory of electric circuits.

### Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order

Piven’ A. L., Rutkas A. G., Vlasenko L. A.

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1484-1500

In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators *A* _{ j } (generally speaking, the operator coefficient *A* _{ n } of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations.

### On the Construction and Growth of Solutions of Degenerate Functional Differential Equations of Neutral Type

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1443-1451

We consider degenerate linear functional differential equations in Banach spaces and construct solutions of exponential and hyperexponential growth. We establish conditions for the unique solvability of an initial-value problem and describe the set of initial functions. The results are applied to partial differential equations with time delay