Artículo
Partial Differential Equations with Delayed Random Perturbations: Existence, Uniqueness and Stability of Solutions
Autor/es | Caraballo Garrido, Tomás
Real Anguas, José |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 1993 |
Fecha de depósito | 2015-04-08 |
Publicado en |
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Resumen | We consider a stochastic non–linear Partial Differential Equation with delay which may be regarded as a perturbed equation. First, we prove the existence and the uniqueness of solutions. Next, we obtain some stability ... We consider a stochastic non–linear Partial Differential Equation with delay which may be regarded as a perturbed equation. First, we prove the existence and the uniqueness of solutions. Next, we obtain some stability results in order to prove the following: if the unperturbed equation is exponentially stable and the stochastic perturbation is small enough then, the perturbed equations remains exponentially stable. We impose standard assumptions on the differential operators and we use strong and mild solutions. |
Cita | Caraballo Garrido, T. y Real Anguas, J. (1993). Partial Differential Equations with Delayed Random Perturbations: Existence, Uniqueness and Stability of Solutions. Stochastic Analysis and Applications, 1 (11), 497-511. |
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