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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 ...
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Analysis of a stochastic 2D–Navier-Stokes model with infinite delay
(Springer, 2019-12)
Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics are established. The existence and uniqueness of solutions in the case of unbounded (infinite) delay ...
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Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution
(American Institute of Mathematical Sciences, 2017-07)
In this paper, the existence of solution for a p-Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal ...
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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 ...
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Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models
(Springer, 2015-04)
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to ...
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Stability results for 2D Navier-Stokes equations with unbounded delay
(Elsevier, 2018-12-05)
Some results related to 2D Navier-Stokes equations when the external force contains hereditary characteristics involving unbounded delays are analyzed. First, the existence and uniqueness of solutions is proved by Galerkin ...
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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 ...
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Almost periodic and almost automorphic solutions of linear differential equations
(2010)
We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear non-homogeneous di erential (or di erence) equation in a Banach space, with almost periodic (respectively, ...