Attractors for non-autonomous retarded lattice dynamical systems
AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.
Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity
In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.
ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS
In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.
On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables
In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.
Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities
AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise.We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.
On the connectedness of the attainability set for lattice dynamical systems
We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for lattice dynamical systems in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property, we can check that the global attractor of the multivalued semiflow generated by such system is connected.
Random resampling numerical simulations applied to a SEIR compartmental model
AbstractIn this paper, we apply resampling techniques to a modified compartmental SEIR model which takes into account the existence of undetected infected people in an epidemic. In particular, we implement numerical simulations for the evolution of the first wave of the COVID-19 pandemic in Spain in 2020. We show, by using suitable measures of goodness, that the point estimates obtained by the bootstrap samples improve the ones of the original data. For example, the relative error of detected currently infected people is equal to 0.061 for the initial estimates, while it is reduced to 0.0538 for the mean over all bootstrap estimated series.
On the Kneser property for reaction–diffusion equations in some unbounded domains with an -valued non-autonomous forcing term
Abstract In this paper, we prove the Kneser property for a reaction–diffusion equation on an unbounded domain satisfying the Poincare inequality with an external force taking values in the space H − 1 . Using this property of solutions we check also the connectedness of the associated global pullback attractor. We study also similar properties for systems of reaction–diffusion equations in which the domain is the whole R N . Finally, the results are applied to a generalized logistic equation.
Breve apuntamiento de los motivos legales que acreditan la justicia que assiste à Don Joseph Folch y Pellizer, Presbitero, en el pleyto que contra el suscitaron Joseph Valero, y Liticonsortes, herederos en segundo lugar de Doña Angela Garcia, primer consorte de Don Juan Bautista Folch, Padre de dicho Don Joseph. Pretendiendo 1981. lib. que como à heredero de su Padre les restaria deviendo à cumplimiento del Dote, y herencia de la referida Doña Angela Garcia.
A la part superior de la port.: "Jesus, Maria, Joseph, y S. Francisco de Paula" Signat al final: "Dr. Luciano Sulroca" Port. orlada Grav. xil. enmarcat de la Mare de Déu i ànimes del Purgatori a la port Caplletra ornada al començament del text Sign.: [A]2, B-E2 Notes al marge Reclams
On the Kneser property for reaction–diffusion systems on unbounded domains
Abstract We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for reaction–diffusion systems on unbounded domains in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property we obtain that the global attractor of such systems is connected. Finally, these results are applied to the complex Ginzburg–Landau equation.