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Addendum To "Global Attractors for Multivalued Random Dynamical Systems'' [Nonlinear Analysis 48(2002) 805-829]
(2005)
The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work
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Stability of some turbulent vertical models for the ocean mixing boundary layer
(Elsevier, 2008-02)
We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions.
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Time and space parallelization of the Navier-Stokes equations
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2005)
In this paper, we will be mainly concerned with a parallel algorithm (in time and space) which is used to solve the incompressible Navier-Stokes problem. This relies on two main ideas: (a) a splitting of the main differential ...
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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 ...
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Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems
(Elsevier, 2018)
This paper investigates the link between the null controllability property for some abstract parabolic problems and an inequality that can be seen as a quantified Fattorini-Hautus test. Depending on the hypotheses made on ...
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On some models describing cellular movement: The macroscopic scale
(Sociedad Española de Matemática Aplicada, 2009-09)
Along this work we will consider several models of partial differential equations that describe cellular movement. We will introduce some mathematical techniques in order to describe the behaviour of the solutions of these models.
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On an iterative method for approximate solutions of a generalized Boussinesq model
(Birkhäuser, 2011-03)
An iterative method is proposed for nding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature dependent ...
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Cooperative systems with any number of species
(Brown University, 2003-12)
In this paper we study the positive solutions of a cooperative system of any number of equations which considers the case of the slow diffusion and includes the Lotka-Volterra model. We determine conditions of existence of ...
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Numerical comparisons of finite element stabilized methods for a 2D vortex dynamics simulation at high Reynolds number
(Elsevier, 2019-02-10)
In this paper, we consider up-to-date and classical Finite Element (FE) stabilized methods for timedependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different ...
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On the controllability of the heat equation with nonlinear boundary Fourier conditions
(Elsevier, 2004-01-20)
In this paper we analyze the approximate and null controllability of the classical heat equation with nonlinear boundary conditions of the form ∂y ∂n + f(y) = 0 and distributed controls, with support in a small set. We ...