A sufficient condition for exponential dichotomy of parabolic evolution equations (Q2708560)

The note establishes the exponential dichotomy of the abstract Cauchy problem NEWLINE\[NEWLINE{{d}\over{dt}}u(t)=A(t)u(t),\quad t\geq s,\qquad u(s)=x,NEWLINE\]NEWLINE assuming that \(A(t),\) \(t\in {\mathbb{R}},\) generates an analytic semigroup \((e^{\tau A(t)})_{\tau\geq 0}\) having exponential dichotomy and and \(A(\cdot)^{-1}\) satisfies a suitable Hölder condition with a small constant.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00037].