Abstract
We prove Holder-continuous dependence results for the difference between solutions of certain ill-posed and approximate well-posed problems in both Hilbert and Banach spaces. We use operator-theoretic methods, including C-semigroups, to treat the abstract Cauchy problem $\frac{du}{dt} = Au, u(0) = \chi, 0 \leq t < T,$ where the operator $-A$ is the infinitesimal generator of a holomorphic semigroup.
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