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Artículo
Semilinear problems with right-hand sides singular at u = 0 which change sign
(Elsevier, 2021-06-01)
The present paper is devoted to the study of the existence of a solution u for a quasilinear second order differential equation with homogeneous Dirichlet conditions, where the right-hand side tends to infinity at u = 0u=0. ...
Artículo
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal
(SIAM, 2021-08-05)
In this paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the ...
Artículo
On terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motions
(IOS Press, 2021-06-09)
In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard Brownian motion and fractional Brownian motion with Hurst parameter h ∈ ( 1/2 , 1) separately. For each ...
Artículo
Switching Controls for Analytic Semigroups and Applications to Parabolic Systems
(SIAM, 2021-08-05)
In this work, we extend the analysis of the problem of switching controls proposedin [E. Zuazua,J. Eur. Math. Soc. (JEMS), 13 (2011), pp. 85--117]. The problem asks the followingquestion: Assuming that one can control a ...
Artículo
Bi-objective optimal control of some PDEs: Nash equilibria and quasi-equilibria
(E.D.P. Sciences, 2021-05-05)
This paper deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. Speci - cally, we look for Nash equilibria ...
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
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 ...
Artículo
Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics
(AIMS Press, 2021-02-04)
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random fluctuations on the input flow, which are modeled by means of the well-known Ornstein-Uhlenbeck ...
Artículo
On the uniform controllability for a family of non-viscous and viscous Burgers- α systems
(E.D.P. Sciences, 2021-06-24)
In this paper we study the global controllability of families of the so called non-viscous and viscous Burgers- systems by using boundary and space independent distributed controls. In these equations, the usual convective ...
Artículo
Finite-Dimensionality of Tempered Random Uniform Attractors
(Springer New York, 2021)
Finite-dimensional attractors play an important role in finite-dimensional reduction of PDEs in mathematical modelization and numerical simulations. For non-autonomous random dynamical systems, Cui and Langa (J Differ ...