arXiv subjects
Publications and source records attributed to R. Klyuchnyk.
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal part of the zero-order coefficients vanish at infinity. Moreover, we establish a dissipativity condition in terms of the boundary data and the diagonal part of the zero-order coefficients.
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on $\R$ in the space of continuous periodic functions.
The paper concerns nonlocal time-periodic boundary value problems for first-order Volterra integro-differential hyperbolic systems with boundary inputs. The systems are subjected to integral boundary conditions. Under natural regularity assumptions on the data it is shown that the problems display completely non-resonant behaviour and satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions.
We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of the problems satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions. A crucial ingredient of our analysis is a non-resonance condition, which is formulated in terms of the data responsible for the bijective part of the Fredholm operator. In the case of $2\times 2$ systems with reflection boundary conditions, we provide a criterium for the non-resonant behavior of the system.