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Displaying 461 – 480 of 603

Null controllability of the heat equation in unbounded domains by a finite measure control region

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically $ℝ_{+}$ or $ℝ^{N}$ . Considering an unbounded and disconnected control region of the form $ω : = \cup_{n} ω_{n}$ , we prove two null controllability results: under some technical assumption on the control parts $ω_{n}$ , we prove that every initial datum in some weighted $L^{2}$ space can be controlled to zero by usual control functions, and every initial datum in $L^{2} (Ω)$ can...

Null controllability of the heat equation in unbounded domains by a finite measure control region

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically $ℝ_{+}$ or $ℝ^{N}$ . Considering an unbounded and disconnected control region of the form $ω : = \cup_{n} ω_{n}$ , we prove two null controllability results: under some technical assumption on the control parts $ω_{n}$ , we prove that every initial datum in some weighted L2 space can be controlled to zero by usual control functions, and every initial datum in L2(Ω)...

Null controllability of the heat equation with boundary Fourier conditions: the linear case

Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form $\frac{\partial y}{\partial n} + β y = 0$ . We consider distributed controls with support in a small set and nonregular coefficients $β = β (x, t)$ . For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.

Null exact controllability of the parabolic equations with equivalued surface boundary condition.

Yin, Zhongqi (2006)

Journal of Applied Mathematics and Stochastic Analysis

Null form estimates for $(1 / 2, 1 / 2)$ symbols and local existence for a quasilinear dirichlet-wave equation

Hart F. Smith, Christopher D. Sogge (2000)

Annales scientifiques de l'École Normale Supérieure

Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system

Piero D'Ancona, Damiano Foschi, Sigmund Selberg (2007)

Journal of the European Mathematical Society

We prove almost optimal local well-posedness for the coupled Dirac–Klein–Gordon (DKG) system of equations in $1 + 3$ dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman–Machedon type. It has been known for some time that the Klein–Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.

Null-control and measurable sets

Jone Apraiz, Luis Escauriaza (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the interior and boundary null-controllability of some parabolic evolutions with controls acting over measurable sets.

Null-controllability of one-dimensional parabolic equations

Giovanni Alessandrini, Luis Escauriaza (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.

Null-controllability of some systems of parabolic type by one control force

Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.

Null-controllability of some systems of parabolic type by one control force

Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Numerical algorithms for perspective shape from shading

Michael Breuss, Emiliano Cristiani, Jean-Denis Durou, Maurizio Falcone, Oliver Vogel (2010)

Kybernetika

The Shape-From-Shading (SFS) problem is a fundamental and classic problem in computer vision. It amounts to compute the 3-D depth of objects in a single given 2-D image. This is done by exploiting information about the illumination and the image brightness. We deal with a recent model for Perspective SFS (PSFS) for Lambertian surfaces. It is defined by a Hamilton–Jacobi equation and complemented by state constraints boundary conditions. In this paper we investigate and compare three state-of-the-art...

Numerical analysis of a semi-implicit DDFV scheme for the regularized curvature driven level set equation in 2D

Angela Handlovičová, Dana Kotorová (2013)

Kybernetika

Stability and convergence of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme in 2D for the solution of the regularized curvature driven level set equation is proved. Numerical experiments concerning comparison with exact solution and image filtering problem using proposed scheme are included.

Numerical Analysis of Cavitational Flow-Theory.

Néstor E. Aguilera (1987)

Numerische Mathematik

Numerical analysis of coupling for a kinetic equation

Moulay Tidriri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we introduce a coupled systems of kinetic equations for the linearized Carleman model. We then study the existence theory and the asymptotic behaviour of the resulting coupled problem. In order to solve the coupled problem we propose to use the time marching algorithm. We then develop a convergence theory for the resulting algorithm. Numerical results confirming the theory are then presented.

Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays

Frédérique Laurent (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in...

Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations

William Layton, Nathaniel Mays, Monika Neda, Catalin Trenchea (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing...

Numerical analysis of nonlinear elliptic-parabolic equations

Emmanuel Maitre (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern’s iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).

Numerical analysis of nonlinear elliptic-parabolic equations

Emmanuel Maitre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).

Numerical analysis of semilinear parabolic problems with blow-up solutions.

C. Bandle, H. Brunner (1994)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations

Eduardo Casas, Fredi Tröltzsch (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness...

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