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The initial-boundary value problem for the first order degenerated hyperbolic system

100%

Lavrenyuk S. , Zaręba L.

tom Vol. 33, nr 1

75-82

In this paper we consider the linear hyperbolic system of the first order with degeneracy at x --0 and x -> l. For such system we assume that initial data arę unbounded on the interval (O, l). Some conditions of the uniqueness, existence and stability of solution for the initial-boundary value problem are obtained.

Steady-state analysis for a class of hyperbolic systems with boundary inputs

88%

Bartecki K.

tom Vol. 23, no. 3

295--310

Results of a steady-state analysis performed for a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the system with two state variables and two boundary inputs, the analytical expressions for the steady-state distribution of the state variables are derived, both in the exponential and in the hyperbolic form. The influence of the location of the boundary inputs on the steady-state response is demonstrated. The considerations are illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

Hyperbolic transformation and hyperbolic difference systems

75%

Dosly O. , Pospisil Z.

tom Nr 32

25-48

Transformations of symplectic difference systems (mathematical formula) are investigated. It is shown that symplectic systems satisfying certain additional condition can be transformed (using a transformation that preserves oscillation properties of transformed systems) into the so-called hyperbolic difference system. Basic properties of solutions of hyperbolic systems are established.

Sensors and boundary state reconstruction of hyperbolic systems

63%

Zerrik E. H. , Bourray H. , Ben Hadid S.

2010

tom Vol. 20, no 2

227-238

This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.

New Lyapunov functions for systems with source terms

63%

Gugat M.

tom Vol. 53, No. 1

163--187

Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic functions and study the advantages in the analysis of 2 × 2 systems of balance laws. We present cases connected with the study of the limit of stabilizability, where the new weights provide Lyapunov functions that show exponential stability for a larger set of problem parameters than classical exponential weights. Moreover, we show that sufficiently large time-delays influence the limit of stabilizability in the sense that the parameter set, for which the system can be stabilized becomes substantially smaller. We also demonstrate that the hyperbolic weights are useful in the analysis of the boundary feedback stability of systems of balance laws that are governed by quasilinear hyperbolic partial differential equations.