Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations | Zendy

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Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations

Author(s) -

Michael Gil'

Publication year - 2013

Publication title -

international journal of partial differential equations

Language(s) - English

Resource type - Journals

eISSN - 2356-7082

pISSN - 2314-6524

DOI - 10.1155/2013/207581

Subject(s) - c0 semigroup , mathematics , analytic semigroup , banach space , semigroup , mathematical analysis , operator (biology) , differential equation , generator (circuit theory) , bounded function , stability (learning theory) , partial differential equation , bounded operator , linear differential equation , integrally closed , exponential stability , parabolic partial differential equation , first order partial differential equation , nonlinear system , physics , biochemistry , power (physics) , transcription factor , gene , mechanical engineering , chemistry , engineering , repressor , quantum mechanics , machine learning , computer science

Let be a generator of an exponentially stableoperator semigroup in a Banach space,and let be a linear bounded variable operator. Assuming that is sufficiently small in a certain sense for the equation, we derive exponential stability conditions. Besides, we do not require that for each , the “frozen” autonomous equation is stable. In particular, we considerevolution equations with periodic operator coefficients. These results are applied to partial differential equations

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