Structural Stability for Ill-Posed Problems in Banach Space |
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| Authors: | Karen A Ames Rhonda J Hughes |
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| Institution: | (1) Department of Mathematics, University of Alabama, Huntsville, AL 35899, USA;(2) Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA |
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| 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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