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Linearized stability for nonlinear evolution equations

In: Nonlinear Evolution Equations and Related Topics

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  • Wolfgang M. Ruess

    (Universität Essen, Fachbereich Mathematik)

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.

Suggested Citation

  • Wolfgang M. Ruess, 2003. "Linearized stability for nonlinear evolution equations," Springer Books, in: Wolfgang Arendt & Haïm Brézis & Michel Pierre (ed.), Nonlinear Evolution Equations and Related Topics, pages 361-373, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7924-8_19
    DOI: 10.1007/978-3-0348-7924-8_19
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