Error controlled regularization by projection
The paper is concerned with the inverse Cauchy problem of finding the initial state \(u_0 \in D(A)\), given \(u(t)\) for some \(t>0\), \({\dot u}+Au=0\), \(u(0)=u_0\), where \(A: D(A) \subset X \to X\) is an unbounded operator in a Hilbert space \(X\). The suggested solution method is based on the Dunford integral representation for the semigroup \(S(t)=e^{-tA}\), combined with the application of recent wavelet methods.
scientific article; zbMATH DE number 5134479