Open AccessSpectral Analysis for a Wave/Plate Transmission System
Author(s) -
Chengqiang Wang
Publication year - 2019
Publication title -
advances in mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.283
H-Index - 23
eISSN - 1687-9139
pISSN - 1687-9120
DOI - 10.1155/2019/7849561
Subject(s) - asymptote , eigenvalues and eigenvectors , mathematical analysis , complex plane , mathematics , zero (linguistics) , sequence (biology) , infinity , spectrum (functional analysis) , wave equation , generator (circuit theory) , semigroup , plane (geometry) , physics , geometry , quantum mechanics , linguistics , philosophy , power (physics) , biology , genetics
We are concerned with the transmission system of a 1D damped wave equation and a 1D undamped plate equation. Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which are all located in the open left half of the complex plane; the sequence of eigenvalues has the imaginary axis and another vertical line to the left of the imaginary axis as its asymptote lines; the energy of the system under consideration decreases to zero as time goes to infinity.