Linearized stability for nonlinear evolution equations

Wolfgang M. Ruess ()
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Wolfgang M. Ruess: Universität Essen, Fachbereich Mathematik

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 361-373 from Springer

Abstract: 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.

Keywords: 47135; 47H06; 35R10; 34K20; Accretive operators; nonlinear evolution equations; linearized stability; partial differential delay equations (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_19

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DOI: 10.1007/978-3-0348-7924-8_19

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