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Artículo
Non-Autonomous Attractor for Integro-Differential Evolution Equations
(2009)
We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an ...
Artículo
Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations
(2006)
In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers the stochastic term in the Ito or Stratonovich sense. In particular, we prove that the Stratonovich ...
Artículo
Stochastic Functional Partial Differential Equations: Existence, Uniqueness and Asymptotic Decay Property
(2000)
Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces are established. Suf cient conditions which guarantee the transference of mean square and pathwise ...
Artículo
Attractors for Stochastic Lattice Dynamical Systems with a Multiplicative Noise
(2008)
In this paper, we consider a stochastic lattice di®erential equation with di®usive nearest neighbor interaction, a dissipative nonlinear reaction term, and a multiplicative white noise at each node. We prove the existence ...
Artículo
Invariant Measures and Statistical Solutions of the Globally Modified Navier-Stokes Equations
(2008)
We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, and we investigate the relationship between global attractors, invariant measures, time-average ...
Tesis Doctoral
Existencia, unicidad y comportamiento asintótico en algunos sistemas dinámicos deterministas y estocásticos
(2003-05-23)
La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la Teoría de Atractores. Más concretamente, en el primer bloque de la tesis se presentan resultados ...
Artículo
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
(2004)
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution ...
Artículo
Recent results on stabilization of PDEs by noise
(Sociedad Española de Matemática Aplicada, 2006-12)
This paper is intended to be a brief review on some recent results on the stabilization effect produced by noise in phenomena modelled by partial differential equations. We emphasyse the different effects that distinct ...
Artículo
Stabilization of Stationary Solutions of Evolution Equations by Noise
(2006)
We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic semilinear evolution equations. Our main result shows, in particular, that noise can have a stabilization ...
Artículo
The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations
(2006)
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise ...