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Beschreibung:
A smooth variation of constants formula for semilinear hyperbolic systems is established using a suitable Banach space $X$ of continuous functions together with its sun dual space $X^{\odot \ast}$. It is shown that mild solutions of this variation of constants formula generate a smooth semiflow in $X$. This proves that the stability of stationary states for the nonlinear flow is determined by the stability of the linearized semigroup.