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Structural stability for ill-posed problems in Banach space. (English) Zbl 1109.34041

The authors give Hölder-continuous dependence results on the difference between solutions of certain ill-posed and approximate well-posed problems in Hilbert spaces and Banach spaces. When \(-A\) is the infinitesimal generator of a holomorphic semigroup, they use operator-theoretic methods to study the Cauchy problem \[ \frac{du}{dt} = Au,\;u(0) = x,\quad\text{on }[0, T). \]

MSC:

34G10 Linear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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