# Kengne E.

### Stabilization of the Cauchy problem for integro-differential equations

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1571–1576

In the present paper, we obtain a criterion for the stabilization of the Cauchy problem for an integro-differential equation in the class of functions of polynomial growth γ ≥ 0.

### On the Well-Posedness of a Two-Point Boundary-Value Problem for a System with Pseudodifferential Operators

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1131 – 1136

We investigate the problem of the well-posedness of a boundary-value problem for a system of pseudodifferential equations of arbitrary order with nonlocal conditions. The equation and boundary conditions contain pseudodifferential operators whose symbols are defined and continuous in a certain domain $H ⊂ ℝ_{σ}^m$. A criterion for the existence and uniqueness of solutions and for the continuous dependence of the solution on the boundary function is established.

### Asymptotically Well-Posed Boundary-Value Problems

Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 169-184

In a domain that is the Cartesian product of an interval and a straight line, we investigate a two-point boundary-value problem for partial differential equations. We establish conditions under which this problem is asymptotically well posed in the class of bounded differentiable functions.

### Well-Posed and Regular Nonlocal Boundary-Value Problems for Partial Differential Equations

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1135-1142

The present paper deals with the well-posedness and regularity of one class of one-dimensional time-dependent boundary-value problems with global boundary conditions on the entire time interval. We establish conditions for the well-posedness of boundary-value problems for partial differential equations in the class of bounded differentiable functions. A criterion for the regularity of the problem under consideration is also obtained.

### Perturbation of a Two-Point Problem

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 980-984

We investigate the problem of the effect of integral terms in boundary conditions on the well-posedness of nonlocal boundary-value problems for partial differential equations.

### Classification of nonlocal boundary-value problems on a narrow strip

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 338–346

For a general linear partial differential equation with constant coefficients, we establish a well-posedness criterion for a boundary-value problem on a strip $Π_y = ℝ × [0,Y]$ with an integral in a boundary condition. A complete classification of such problems based on their asymptotic properties as $Y → 0$ is obtained.