On the stability of essential spectra of semigroups generated by one-dimensional hyperbolic systems. (English) Zbl 1542.35245
Summary: This paper provides a new and systematic approach to stability properties of essential spectra or essential types for semigroups generated by hyperbolic systems in one space variable. In particular, we extend a previous theory by A. F. Neves et al. [J. Funct. Anal. 67, 320–344 (1986; Zbl 0594.35009)]. Our construction relies on a fine analysis of the difference of resolvent generators and on results on oscillatory integrals. Applications to stabilization of a Timoshenko beam system and to some discrete kinetic models are given.
MSC:
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 93D23 | Exponential stability |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
Keywords:
hyperbolic systems; stability of essential spectra; stability of essential types; oscillatory integralsCitations:
Zbl 0594.35009References:
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