Orlovsky, Dmitry; Piskarev, Sergey; Spigler, Renato On approximation of inverse problems for abstract hyperbolic equations. (English) Zbl 1410.65232 Taiwanese J. Math. 14, No. 3B, 1145-1167 (2010). Summary: This paper is devoted to the numerical analysis of inverse problems for abstract hyperbolic differential equations. The presentation exploits a general approximation scheme and is based on \(C_0\)-cosine and \(C_0\)-semigroup theory within a functional analysis approach. We consider both discretizations in space as well as in time. The discretization in time is considered under the Krein-Fattorini conditions. Cited in 3 Documents MSC: 65J22 Numerical solution to inverse problems in abstract spaces 65J08 Numerical solutions to abstract evolution equations 34G10 Linear differential equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations 47D09 Operator sine and cosine functions and higher-order Cauchy problems 47N20 Applications of operator theory to differential and integral equations 47N40 Applications of operator theory in numerical analysis PDFBibTeX XMLCite \textit{D. Orlovsky} et al., Taiwanese J. Math. 14, No. 3B, 1145--1167 (2010; Zbl 1410.65232) Full Text: DOI