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On approximation of inverse problems for abstract hyperbolic equations. (English) Zbl 1410.65232

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.

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
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