Variation of constants formula for hyperbolic systems
- Lichtner, Mark
2010 Mathematics Subject Classification
- 35L90 37L05 35B30 58D25 37L50 34K20 34K19
- Semilinear hyperbolic systems, variations of constants formula, sun star calculus, smooth dependence on data, linarized stability, semigroup theory
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.