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On the numerical approximation of a geometric control problem
(Universidad de Barcelona, 1982-09-15)
The purpose of this paper is to introduce a new method for solving an optimun design problem: determining the aerodynamic body of minimun-drag profile at constant velocity in a viscous incompressible fluid. The stationnary ...
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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 ...
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Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design
(Elsevier, 2006-07-15)
In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients and the domains vary arbitrarily. Here, we improve the convergence result given in this paper ...
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Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion
(Society for Industrial and Applied Mathematics, 2008)
We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in density-velocity-pressure formulation), also called the Kazhikhov–Smagulov model. We will prove conditional ...
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Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions
(American Institute of Mathematical Sciences, 2019-06)
We consider the Stokes system in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size ε. On the boundary of the cylinders we prescribe non-homogeneous slip boundary ...
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Asymptotic Behaviour of Solutions for a Three Dimensional System of Globally Modified Navier-Stokes Equations with a Locally Lipschitz Delay Term
(Elsevier, 2013)
Existence, uniqueness, and continuity properties of solutions for a globally modified version of Navier–Stokes equations with finite delay terms within a locally Lipschitz operator are established. Moreover, we also analyze ...
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Upper Semicontinuity of Attractors for Small Random Perturbations of Dynamical Systems
(1998)
The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an ²¡small random term and certain hypotheses are satisfied, the upper ...
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Attractors for semilinear wave equations with localizad damping and external forces
(Cornell University, 2020-01-08)
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of R3 with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global ...
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Asymptotic Exponential Stability of Stochastic Partial Differential Equations with Delay
(1990)
Sufficient conditions for pathwise asymptotic exponential stability of the solution of the stochastic PDE with delay d x t = Ax tdt + B(xp(t)) dwt are given. The assumptions on the operators A and B are essentially the ...
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Existence of weak-renormalized solution for a nonlinear system
(Universidad Complutense de Madrid, 2002)
We prove an existence result for a coupled system of the reactiondiffusion kind. The fact that no growth condition is assumed on some nonlinear terms motivates the search of a weak-renormalized solution.