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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 INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS
(American Mathematical Society, 2020-06-11)
In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal value problem. For an initial value problem, we study local existence, uniqueness, and continuous ...
Artículo
Stability results for neutral stochastic functional differential equations via fixed point methods
(Taylor and Francis, 2020)
In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and ...
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
Nonlocal and nonlinear evolution equations in perforated domains
(Academic Press Inc Elsevier Science, 2020-12-02)
In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form ut(x; t) = R J(x�����y)u(y; t) dy �����h"(x)u(x; t)+f(x; u(x; t)) with x in a perturbed domain " which is thought ...
Artículo
Strong trajectory statistical solutions and Liouville type equation for dissipative Euler equations
(Elsevier, 2020-01)
The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory statistical solutions for two-dimensional dissipative Euler equations. Further, it is established that ...
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
On some geometric inverse problems for nonscalar elliptic systems
(Elsevier, 2020-07-02)
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the ...