WIAS Preprint No. 1212, (2007)

Variation of constants formula for hyperbolic systems



Authors

  • Lichtner, Mark

2010 Mathematics Subject Classification

  • 35L90 37L05 35B30 58D25 37L50 34K20 34K19

Keywords

  • Semilinear hyperbolic systems, variations of constants formula, sun star calculus, smooth dependence on data, linarized stability, semigroup theory

Abstract

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.

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