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Variation of constants formula for hyperbolic systems

Lichtner M.

Journal of Applied Analysis

2009

Vol. 15, nr 1

79-100

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 [wzór]. 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.