# Kirilich V. M.

### Problem without initial conditions for a countable semilinear hyperbolic system of first-order equations

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1043-1055

We derive sufficient conditions for the solvability of the problem without initial conditions for a countable semilinear hyperbolic system of first-order equations and establish conditions for the classical solvability of the initial-boundary value problem for countable hyperbolic systems of semilinear equations of the first-order in a semistrip.

### Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning

Derev’yanko N. V., Kirilich V. M.

Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 185–201

We establish necessary conditions for the optimality of smooth boundary and initial controls in a semilinear hyperbolic system of the first order. The problem adjoint to the original problem is a semilinear hyperbolic system without initial conditions. The suggested approach is based on the use of special variations of continuously differentiable controls. The existence of global generalized solutions for a semilinear first-order hyperbolic system in a domain unbounded in time is proved. The proof is based on the use of the Banach fixed-point theorem and a space metric with weight functions.

### Quasilinear hyperbolic stefan problem with nonlocal boundary conditions

Andrusyak R. V., Burdeina N. O., Kirilich V. M.

Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1173–1199

Using the method of contracting mappings, we prove, for small values of time, the existence and uniqueness of a generalized Lipschitz solution of a mixed problem with unknown boundaries for a hyperbolic quasilinear system of first-order equations represented in terms of Riemann invariants with nonlocal (nonseparated and integral) boundary conditions.

### Oscillations of a diaphragm under the action of pulse forces

Kirilich V. M., Myshkis A. D., Prokhorenko M. V.

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1148-1153

We investigate the problem of the existence of periodic solutions of the problem of oscillations of a diaphragm with friction and pulse feedback in the case where the times of pulse action are determined by a solution of the system.

### Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations

Andrusyak R. V., Burdeina N. O., Kirilich V. M.

Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 867-891

Using the method of characteristics and the method of contracting mappings, we establish the local classical solvability of a problem for a hyperbolic system of quasilinear first-order equations with moving boundaries and nonlinear boundary conditions. Under additional assumptions on the monotonicity and sign constancy of initial data and a restriction on the growth of the right-hand sides of the system, we formulate sufficient conditions for the global classical solvability of the problem.

### Hyperbolic stefan problem in a curvilinear sector

Berehova H. I., Kirilich V. M.

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1684–1689

The problem with unknown boundaries for a first-order semilinear hyperbolic system is studied in the case where the curve of definition of the initial conditions degenerates to a point. An existence and uniqueness theorem for a classical solution of the problem is proved for small *t*.

### A nonlocal stefan-type problem for a first-order hyperbolic system

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 121-124

### Problems without initial conditions with integral restrictions for hyperbolic equations and systems on a line

Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 722-727