Browsing Past Topics (PT) by Title
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2D euler shape design on nonregular flows using adjoint rankinehugoniot relations
(AIAA Journal, 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 class of CTRWs: Compound fractional poisson processes
(Fractional Dynamics: Recent Advances, 20111231)This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. It begins with the characterization of a wellknown Lévy process: The compound Poisson process. The semiMarkov extension ... 
A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations
(Central European Journal of Mathematics, 20131231)We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different ... 
A functional limit theorem for stochastic integrals driven by a timechanged symmetric sigmastable Levy process
(Stochastic Processes and their Applications, 20141231)Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the $M_1$topology of a sequence of stochastic integrals of a deterministic function driven by a timechanged ... 
A Hyperbolic system and the cost of the controllability for the Stokes system
(Computational and Applied Mathematics, 20141231)This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time $T$ is of order $e^{CIT} ... 
A hyperbolic system and the cost of the null controllability for the Stokes system
(Computational and Applied Mathematics, 20151231)This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time $T$ is of order $e^{C/T}$ ... 
A kinetic scheme for transient mixed flows in non uniform closed pipes: A global manner to upwind all the source terms
(Journal of Scientific Computing, 20111231)We present a numerical kinetic scheme for an unsteady mixed pressurized and free surface model. This model has a source term depending on both the space variable and the unknown U of the system. Using the Finite Volume and ... 
A lower bound on local energy of partial sum of eigenfunctions for LaplaceBeltrami operators
(ESAIM  Control, Optimisation and Calculus of Variations, 20131231)In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for LaplaceBeltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This ... 
A mathematical model for unsteady mixed flows in closed water pipes
(Science China Mathematics, 20121231)We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes. In the case of free surface incompressible flows, the FSmodel is formally obtained, using formal ... 
A multilayer method for the hydrostatic NavierStokes equations: A particular weak solution
(Journal of Scientific Computing, 20141231)In this work we present a multilayer approach to the solution of nonstationary 3D NavierStokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal ... 
A note on complete hyperbolic operators with logZygmund coefficients
(Fourier Analysis  Pseudodifferential Operators, TimeFrequency Analysis and Partial Differential Equations'', M. Ruzhansky and V. Turunen eds., Trends in Mathematics, Birkh\\\auser, Basel.", 20141231)The present paper is the continuation of the recent work [7], and it is devoted to strictly hyperbolic operators with nonregular coefficients. We focus here on the case of complete operators whose secondorder coefficients ... 
A penalization and regularization technique in shape optimization problems
(SIAM Journal on Control and Optimization, 20131231)We consider shape optimization problems, where the state is governed by elliptic partial differential equations. Using a regularization technique, unknown shapes are encoded via shape functions, turning the shape optimization ... 
A posteriori error control for fully discrete cranknicolson schemes
(SIAM Journal on Numerical Analysis, 20121231)We derive residualbased a posteriori error estimates of optimal order for fully discrete approximations for linear parabolic problems. The time discretization uses the Crank Nicolson method, and the space discretization ... 
A quantitative boundary unique continuation for stochastic parabolic equations
(Journal of Mathematical Analysis and Applications, 20131231)This paper is addressed to the boundary unique continuation property for forward stochastic parabolic equations, that is, to determine the value of the solution by virtue of the observation on an arbitrary open subset of ... 
A regularity property for Schrödinger equations on bounded domains
(Revista Matematica Complutense, 20131231)We give a regularity result for the free Schrödinger equations set in a bounded domain of ℝ N which extends the 1dimensional result proved in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520554, 2010) with different ... 
A result concerning the global approximate controllability of the NavierStokes system in dimension 3
(Journal des Mathematiques Pures et Appliquees, 20121231)In this paper we deal with the threedimensional NavierStokes system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some ... 
A splitting method for the nonlinear Schrödinger equation
(Journal of Differential Equations, 20111231)We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical wellposedness L2(Rd)theory. More precisely, we prove that ... 
A systematic method for building smooth controls for smooth data
(Discrete and Continuous Dynamical Systems  Series B, 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 ... 
A Systematization of the Unscented Kalman Filter Theory
(IEEE Transactions on Automatic Control, 20151231)In this paper, we propose a systematization of the (discretetime) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide ... 
A uniform controllability result for the KellerSegel system
(Asymptotic Analysis, 20151231)In this paper we study the controllability of the KellerSegel system approximating its parabolicelliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the ...