Existence of exponentially attracting stationary solutions for delay evolution equations

We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution exponentially stable, for which we use a general random fixed point theorem for general cocycles...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Garrido Atienza, María José, Schmalfuss, Björn
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23663
Acceso en línea:http://hdl.handle.net/11441/23663
https://doi.org/10.3934/dcds.2007.18.271
Access Level:acceso abierto
Palabra clave:Cocycle
Random dynamical systems
Stationary solutions
Delay equations
Exponential stability
Descripción
Sumario:We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution exponentially stable, for which we use a general random fixed point theorem for general cocycles. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly, by means of the theory of random dynamical systems and their conjugation properties.