Publikation:

Exponential stability for wave equations with non-dissipative damping

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2008

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Muñoz Rivera, Jaime E.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-96367
DOI (zitierfähiger Link)
https://doi.org/10.1016/j.na.2007.02.022
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Published

Erschienen in

Nonlinear Analysis : theory, methods & applications. 2008, 68(9), pp. 2531-2551. ISSN 0362-546X. eISSN 1873-5215. Available under: doi: 10.1016/j.na.2007.02.022

Zusammenfassung

We consider the nonlinear wave equation utt−σ(ux)x+a(x)ut=0 in a bounded interval (0, L) C R1. The function a is allowed to change sign, but has to satisfy a = 1/LR L 0 a(x)dx > 0. For this non-dissipative situation we prove the exponential stability of the corresponding linearized system for: (I) possibly large ||a||L∞ with small ||a(·) − a||L2, and (II) a class of pairs (a,L) with possibly negative moment R L0 a(x) sin2(pi x/L) dx. Estimates for the decay rate are also given in terms of a. Moreover, we show the global existence of smooth, small solutions to the corresponding nonlinear system if, additionally, the negative part of a is small enough.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Indefinite damping, Wave equation, Exponential stability

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ISO 690MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2008. Exponential stability for wave equations with non-dissipative damping. In: Nonlinear Analysis : theory, methods & applications. 2008, 68(9), pp. 2531-2551. ISSN 0362-546X. eISSN 1873-5215. Available under: doi: 10.1016/j.na.2007.02.022
BibTex
@article{MunozRivera2008Expon-737,
  year={2008},
  doi={10.1016/j.na.2007.02.022},
  title={Exponential stability for wave equations with non-dissipative damping},
  number={9},
  volume={68},
  issn={0362-546X},
  journal={Nonlinear Analysis : theory, methods & applications},
  pages={2531--2551},
  author={Muñoz Rivera, Jaime E. and Racke, Reinhard}
}
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