The conservative model of a dissipative dynamical system

Let R_σ be the response operator of a dissipative dynamical system (DS) governed by the equation u_tt−σu_t−u_xx=0, x>0, where σ=σ(x)≧0. Let R_q be the response operator of a conservative DS governed by the equation u_tt−u_xx+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 R_σ=R_q. Bibliography: 10 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 21–35. Translated by M. I. Belishev.