Browsing Former Research Lines by Author "Zuazua, E."
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2D euler shape design on nonregular flows using adjoint rankinehugoniot relations
Baeza, A.; Castro, C.; Palacios, F.; Zuazua, E. (20091231)Optimal aerodynamic shape design aims to find the minimum of a functional that describes an aerodynamic property, by controlling the partial differential equation modeling the dynamics of the flow that surrounds an aircraft, ... 
A systematic method for building smooth controls for smooth data
Ervedoza, S.; Zuazua, E. (20101231)We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z0 in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability ... 
Approximating travelling waves by equilibria of nonlocal equations
Arrieta, J.M.; LópezFernández, M.; Zuazua, E. (20121231)We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a nonlocal evolution ... 
Asymptotic expansions for anisotropic heat kernels
Ignat, L.I.; Zuazua, E. (20131231)We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lpspaces. We mainly address two model examples. In the first one, the diffusivity ... 
Asymptotic limits and stabilization for the 1D nonlinear MindlinTimoshenko system
Araruna, F.D.; E Silva, P.B.; Zuazua, E. (20101231)This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
Asymptotics and stabilization for dynamic models of nonlinear beams
Ranina, F.D.; Silva, P.B.E.; Zuazua, E. (20101231)We prove that the von Kármán model for vibrating beams can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
Averaged control
Zuazua, E. (20141231)We analyze the problem of controlling parameterdependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First ... 
Averaged control and observation of parameterdepending wave equations
Lazar, M.; Zuazua, E. (20141231)We analyze the problem of averaged observability and control of wave equations.This topic is motivated by the control of parameterdependent systems of wave equations. We look for controls ensuring the controllability of ... 
Blowup for a timeoscillating nonlinear heat equation
Cazenave, T.; Escobedo, M.; Zuazua, E. (20131231)In this paper, we study a nonlinear heat equation with a periodic time oscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according ... 
Boundary stabilization of numerical approximations of the 1D variable coefficients wave equation: A numerical viscosity approach
Marica, A.; Zuazua, E. (20141231)In this paper, we consider the boundary stabilization problem associated to the 1 d wave equation with both variable density and diffusion coefficients and to its finite difference semidiscretizations. It is wellknown ... 
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
Privat, Y.; Trélat, E.; Zuazua, E. (20151231)We consider the homogeneous wave equation on a bounded open connected subset Î© of IRn. Some initial data being specified, we consider the problem of determining a measurable subset Ï‰ of Î© maximizing the L2norm of the ... 
Continuous adjoint approach for the spalartallmaras model in aerodynamic optimization
BuenoOrovio, A.; Castro, C.; Palacios, F.; Zuazua, E. (20121231)In this paper, the continuous adjoint method to compute shape sensitivities in aerodynamic design with turbulence modeling is described and developed. The focus is on compressible flows described by the Reynoldsaveraged ... 
Control and stabilization of waves on 1d networks
Zuazua, E. (20131231)We present some recent results on control and stabilization of waves on 1d networks.The fine timeevolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a ... 
Control of 2D scalar conservation laws in the presence of shocks
Lecaros, R.; Zuazua, E. (20160101)We analyze a model optimal control problem for a 2D scalar conservation lawthe socalled inverse design problemwith the goal being to identify the initial datum leading to a given final time configuration. The presence ... 
Convergence of a twogrid algorithm for the control of the wave equation
Ignat, L.I.; Zuazua, E. (20091231)We analyze the problem of boundary observability of the finitedifference space semidiscretizations of the 2d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ... 
Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
Ignat, L.I.; Zuazua, E. (20121231)This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and ... 
Dispersion for 1d Schrödinger and wave equations with bv coefficients
Beli, N.; Ignat, L.I.; Zuazua, E. (20160101)In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ... 
Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach
Zhang, X.; Zheng, C.; Zuazua, E. (20101231)In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space ... 
Flux identification for 1d scalar conservation laws in the presence of shocks
Castro, C.; Zuazua, E. (20111231)We consider the problem of flux identification for 1d scalar conservation laws formulating it as an optimal control problem. We introduce a new optimization strategy to compute numerical approximations of minimizing fluxes. ... 
Generation of twodimensional water waves by moving bottom disturbances
Nersisyan, H.; Dutykh, D.; Zuazua, E. (20141231)In this study we investigate the potential and limitations of the wave genera tion by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape ...