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On stability estimates in multidimensional inverse problems for differential equations. (English. Russian original) Zbl 0679.35085
Sov. Math., Dokl. 38, No. 3, 614-617 (1989); translation from Dokl. Akad. Nauk SSSR 303, No. 4, 803-806 (1988).
Let A be a uniformly elliptic operator on a domain \(\Omega\) in \({\mathbb{R}}^ n\), B be a matrix of first order partial differential operators, \(\rho\) be a matrix coefficient function. The inverse problem of determining the vector functions u and q in the parabolic (hyperbolic) systems \[ [(\partial^{(2)}/\partial t^{(2)}+A)I+B]u=\rho q+f \] from overdetermined boundary data is considered. For sufficiently large observation time, stability estimates are given.
Reviewer: H.W.Engl

35R30 Inverse problems for PDEs
35B35 Stability in context of PDEs
35K40 Second-order parabolic systems
86A99 Geophysics
35L55 Higher-order hyperbolic systems