Structural stability for ill-posed problems in Banach space (Q2505022)

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 \[ \frac{du}{dt} = Au,\;u(0) = x,\quad\text{on }[0, T). \]