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Artículo
Upper Semicontinuity of Attractors for Small Random Perturbations of Dynamical Systems
(1998)
The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an ²¡small random term and certain hypotheses are satisfied, the upper ...
Artículo
Asymptotic Exponential Stability of Stochastic Partial Differential Equations with Delay
(1990)
Sufficient conditions for pathwise asymptotic exponential stability of the solution of the stochastic PDE with delay d x t = Ax tdt + B(xp(t)) dwt are given. The assumptions on the operators A and B are essentially the ...
Artículo
Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257
(Elsevier [Commercial Publisher], 2021-05-01)
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. López-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun ...
Artículo
On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems
(2014)
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then ...
Ponencia
Pullback attractors to analyze the effect of random and stochastic disturbances in the chemostat model
(2018)
In this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern techniques concerning the theory of random dynamical systems. Particularly, the existence and ...
Artículo
Nontrivial equilibrium solutions and general 2 stability for stochastic evolution equations with pantograph delay and tempered fractional noise∗
(SIAM, 2022-10-07)
In this paper, we study the full compressible Navier--Stokes system in a bounded domain Ω⊂R3 , where the viscosity and heat conductivity depend on temperature in a power law (θb for some constant b>0 ) of Chapman--Enskog. ...
Artículo
Hyers-Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems
(De Gruyter, 2019-09)
In this paper, we prove some existence, uniqueness and Hyers-Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is ...
Artículo
Chemostats with random inputs and wall growth
(John Wiley & Sons, 2015-03-12)
Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded as an idealization of nature to study competition modeling of mathematical biology. The simple form ...
Artículo
Autonomous and non-autonomous attractors for differential equations with delays
(2005)
The asymptotic behaviour of some types of retarded differential equations, with both variable and distributed delays, is analyzed. In fact, the existence of global attractors is established for different situations: with ...
Artículo
Transportation inequalities for coupled systems of stochastic delay evolution equations with a fractional Brownian motion
(Taylor and Francis Online, 2021-02-17)
We prove an existence and uniqueness result of mild solution for a system of stochastic semilinear differential equations with fractional Brownian motions and Hurst parameter H < 1/2. Our approach is based on Perov’s fixed ...