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  • 1
    Electronic Resource
    Electronic Resource
    Théorèmes de Trace et d'Interpolation (IV) (1963)
    Springer
    Mathematische Annalen 151 (1963), S. 42-56 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01343324
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  • 2
    Electronic Resource
    Electronic Resource
    Nouvelles Methodes en Contrôle Impulsionnel (1975)
    Springer
    Applied mathematics & optimization 1 (1975), S. 289-312 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Abstract This article develops a general methodology for solving optimal impulse control problems. The basic tool is the concept of quasi-variational inequalities. These inequalities play for impulse control a part similar to Hamilton-Jacobi-Bellman equations for continuous control theory. The concept of quasi variational inequality generalizes the concept of variational inequality. One gives a theorem of existence of a solution of a quasi variational inequality and one shows that it is possible to deduce from it an optimal solution for a problem of impulse control.
    Notes: Resumé On présente dans cet article une méthodologie générale de traitement des problèmes de contrôle impulsionnel, fondée sur l'étude systématique des inéquations quasi variationnelles. Celles-ci jouent pour le contrôle impulsionnel un rôle analogue à celui des équations de Hamilton-Jacobi-Bellman pour le contrôle continu. La notion d'inéquation quasi-variationnelle généralise celle d'inéquation variationnelle. On donne un théorème d'existence de solution d'une inéquation quasi-variationnelle et on montre que cette solution permet de construire une solution optimale pour un problème de contrôle impulsionnel.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01447955
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  • 3
    Electronic Resource
    Electronic Resource
    Filtering of distributed parameter systems with pointwise disturbances (1981)
    Springer
    Applied mathematics & optimization 7 (1981), S. 191-224 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider in this article a filtering problem for a linear distributed parameter system where the input disturbances are located in points instead of being distributed. The observation process is assumed to be distributed inside the domain. Although formally one can derive equations for the Kalman filter and the Riccati equation, the complete justification of these equations leads to problems which cannot be solved by standard methods, in the sense that some new functional spaces need to be introduced. The objective of the paper is to give a rigorous treatment of this nonclassical filtering problem, which is relevant for applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442116
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  • 4
    Electronic Resource
    Electronic Resource
    Inéquations en thermoélasticité et magnétohydrodynamique (1972)
    Springer
    Archive for rational mechanics and analysis 46 (1972), S. 241-279 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250512
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  • 5
    Electronic Resource
    Electronic Resource
    On exact and approximate boundary controllabilities for the heat equation: A numerical approach (1994)
    Springer
    Journal of optimization theory and applications 82 (1994), S. 429-484 
    Details
    ISSN: 1573-2878
    Keywords: Heat equation ; boundary control problems ; adjoint equations ; Hilbert uniqueness method ; regularization ; penalty ; convex duality ; variational inequalities ; conjugate gradient methods ; finite difference methods ; finite element methods ; operator splitting algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present article is concerned with the numerical implementation of the Hilbert uniqueness method for solving exact and approximate boundary controllability problems for the heat equation. Using convex duality, we reduce the solution of the boundary control problems to the solution of identification problems for the initial data of an adjoint heat equation. To solve these identification problems, we use a combination of finite difference methods for the time discretization, finite element methods for the space discretization, and of conjugate gradient and operator splitting methods for the iterative solution of the discrete control problems. We apply then the above methodology to the solution of exact and approximate boundary controllability test problems in two space dimensions. The numerical results validate the methods discussed in this article and clearly show the computational advantage of using second-order accurate time discretization methods to approximate the control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192213
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  • 6
    Electronic Resource
    Electronic Resource
    Measures of controllability (1994)
    Springer
    Georgian mathematical journal 1 (1994), S. 47-52 
    Details
    ISSN: 1572-9176
    Keywords: 49J20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce here a new notion, the measure ofcontrollability aimed at expressing that one system is “more controllable” than another one. First estimates are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02315302
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  • 7
    Electronic Resource
    Electronic Resource
    Contribution à un problème de M. M. Picone (1956)
    Springer
    Annali di matematica pura ed applicata 41 (1956), S. 201-219 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Résumé Par une méthode fonctionnelle développée ailleurs (cf. la bibliographie), on apporte dans cet article une contribution à un problème posé parM. M. Picone. On montre que, sur des ouverts dont la frontière est suffisamment régulière, le problème deM. M. Picone (et même un type plus général de problèmes aux limites) admet une solution unique, les conditions aux limites étant prises « en moyenne » (cf. No 6 pour les définitions précises).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411668
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  • 8
    Electronic Resource
    Electronic Resource
    Optimisation pour certaines classes d'équations d'évolution non linéaires (1966)
    Springer
    Annali di matematica pura ed applicata 72 (1966), S. 275-293 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Résumé Comme dans l'Introduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02414339
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  • 9
    Electronic Resource
    Electronic Resource
    Espaces du type de Gevrey et problèmes aux limites pour diverses classes d'équations d'évolution (1966)
    Springer
    Annali di matematica pura ed applicata 72 (1966), S. 343-394 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Résumé Le travail est résumé dans l'introduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02414344
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  • 10
    Electronic Resource
    Electronic Resource
    Espaces de fonctions et distributions du type de Gevrey et problèmes aux limites paraboliques (1965)
    Springer
    Annali di matematica pura ed applicata 68 (1965), S. 341-417 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Résumé Le travail est résumé dans l'Introduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411029
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