Geodesic
The conservative model of a~dissipative dynamical system
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 25, Tome 230 (1995), pp. 21-35

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Let $R_\sigma$ be the response operator of a dissipative dynamical system (DS) governed by the equation $u_{tt}+\sigma u_t-u_{xx}=0$, $x>0$, where $\sigma=\sigma(x)\ge0$. Let $R_q$ be the response operator of a conservative DS governed by the equation $u_{tt}-u_{xx}+q(x)u=0$, $x>0$, where $q=q(x)$ is real. We demonstrate that for any dissipative DS there exists a unique conservative DS (the “model”) such that $R_\sigma=R_q$ is valid. Bibl. 10 titles. 
@article{ZNSL_1995_230_a2,
     author = {M. I. Belishev},
     title = {The conservative model of a~dissipative dynamical system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--35},
     publisher = {mathdoc},
     volume = {230},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_230_a2/}
}
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M. I. Belishev. The conservative model of a~dissipative dynamical system. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 25, Tome 230 (1995), pp. 21-35. http://geodesic.mathdoc.fr/item/ZNSL_1995_230_a2/