Abstract
We present a general principle of linearized stability at an equilibrium point for the Cauchy problem \( \dot{u}(t) + Au(t) \ni 0,t \geqslant 0,u(0) = u0 \) for an ω-accretive, possibly multivalued, operator A ⊂ Xx X in a Banach space X that has a linear ‘resolvent-derivative’ Ã ⊂ X x X. The result is applied to derive linearized stability results for the case of A = (B + G) under ‘minimal’ differentiability assumptions on the operators B ⊂ X x X and G: cl D(B) → at the equilibrium point, as well as for partial differential delay equations.
To the memory of Philippe Bénilan
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Ruess, W.M. (2003). Linearized stability for nonlinear evolution equations. In: Arendt, W., Brézis, H., Pierre, M. (eds) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7924-8_19
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DOI: https://doi.org/10.1007/978-3-0348-7924-8_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7107-4
Online ISBN: 978-3-0348-7924-8
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