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The conservative model of a dissipative dynamical system

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Abstract

Let Rσ be the response operator of a dissipative dynamical system (DS) governed by the equation utt−σut−uxx=0, x>0, where σ=σ(x)≧0. Let Rq be the response operator of a conservative DS governed by the equation utt−uxx+qu=0, x>0, where q=q(x) is real. We demonstrate that for any dissipative DS there exists a unique conservative DS (the “model”) such that Rσ=Rq. Bibliography: 10 titles.

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References

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Authors
  1. M. I. Belishev
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 21–35.

Translated by M. I. Belishev.

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Belishev, M.I. The conservative model of a dissipative dynamical system. J Math Sci 91, 2711–2721 (1998). https://doi.org/10.1007/BF02433986

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  • DOI: https://doi.org/10.1007/BF02433986

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