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Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping

Hong Gimyong, Hong Hakho

Journal of Applied Analysis

2023

Vol. 29, nr 1

77--90

We are concerned with the stability of a 1-D coupled Rayleigh beam-string transmission system.We obtain the polynomial decay rate t−1 or the exponential decay rate for the given transmission system whether the frictional damping is only effective in the beam part or the string part, respectively. This paper generalizes the recent result in [Y.-F. Li, Z.-J. Han and G.-Q. Xu, Explicit decay rate for coupled string-beam system with localized frictional damping, Appl. Math. Lett. 78 (2018), 51-58]. The main ingredient of the proof is some careful analysis for the Rayleigh beam and string transmission system.

On some elliptic operator of order one

Kołakowski J. H.

Biuletyn Wojskowej Akademii Technicznej

2008

Vol. 57, nr 4

95-99

The purpose of this paper is to determine explicitly wellposed transmission problems for some elliptic system. It is well known that for this system there is no wellposed boundary value problem in any bounded domain in R⁴.

Celem tej pracy jest wydzielenie pewnej klasy dobrze postawionych zagadnień transmisji dla operatora eliptycznego o którym wiadomo, że nie istnieje dla niego dobrze postawione zagadnienie brzegowe i to na dowolnym obszarze.

Transmission problems for the Helmholtz equation for a rectilinear-circular lune

Denysenko V.

Opuscula Mathematica

2007

Vol. 27, no. 2

197-203

The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.