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Energy decay of damped systems
Author(s) -
Veselić K.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310140
Subject(s) - semigroup , bounded function , pencil (optics) , quadratic equation , exponential decay , mathematics , operator (biology) , upper and lower bounds , mathematical analysis , range (aeronautics) , exponential function , partial differential equation , simple (philosophy) , physics , quantum mechanics , geometry , biochemistry , chemistry , materials science , philosophy , epistemology , repressor , transcription factor , composite material , gene
Abstract We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.