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Inverse problem for a wave equation with a piecewise-constant coefficient. (English. Russian original) Zbl 0784.35121
Sib. Math. J. 33, No. 3, 452-461 (1992); translation from Sib. Mat. Zh. 33, No. 3, 101-111 (1992).
The paper concerns the determination of $$C(x)$$ in the one-dimensional wave equation $$u_{tt}=u_{xx}/c^ 2(x)$$ under the initial condition $$u|_{t<0}=0$$ and boundary condition $$u_ x(0,t)=H(t)$$, and analogous problems in the Lamé equation and Helmholtz equation. Considering an isotropic layered medium in the half-space the coefficient $$c$$ can assumed to be piecewise constant. The additional information is the knowledge of $$\int^ \infty_{-\infty}u_ t(0,t) e^{-i \omega t}dt$$, $$\omega$$ from a finite interval.

##### MSC:
 35R30 Inverse problems for PDEs 35L05 Wave equation 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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##### References:
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