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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
The Lotka-Volterra models with non-local reaction terms
(American Institute of Mathematical Sciences (AIMS), 2022-11)
In this paper we consider a diffusive Lotka-Volterra system including nonlocal terms in the reaction functions. We analyze the main types of interactions between species: competition, predator-prey and cooperation. We ...
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
Statistical solutions and Kolmogorov entropy for the lattice long-wave-short-wave resonance equations in weighted space
(Elsevier, 2023-04-25)
This article studies the lattice long-wave-short-wave resonance equations in weighted spaces. The authors first prove the global well-posedness of the initial value problem and the existence of the pullback attractor for ...
Artículo
Invariant manifolds for stochastic delayed partial differential equations of parabolic type
(Elsevier, 2023-06-12)
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential ...
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
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 ...