THEMES PRINCIPAUX DE RECHERCHE

Systèmes dynamiques:

Equations différentielles. Inclusions différentielles. Systèmes dissipatifs. EDP hyperboliques non-linéaires.

Analyse non-linéaire:

Régularisation et approximation. Analyse convexe. Analyse multivoque.

Optimisation:

Algorithmes de minimisation. Méthodes proximales. Sélection asymptotique d'un optimum particulier.

Mécanique non-régulière:

Problèmes de billard. Théorie des chocs. Frottement de Coulomb et stabilisation en temps fini.

ARTICLES PARUS OU A PARAITRE

• [1] H. Attouch, A. Cabot, P. Redont, The dynamics of elastic shocks via epigraphical regularization
  of a differential inclusion. Barrier and penalty approximations.
  Advances in Math. Sciences and Applications, 12 (2002), no. 1, 273--306.

• [2] A. Cabot, Motion with friction of a heavy particle on a manifold- Applications to Optimization.
  M2AN Mathematical Modelling Numerical Analysis, 36 (2002), no. 3, 505--516.

• [3] A. Cabot, M.-O. Czarnecki, Asymptotic control of pairs of oscillators coupled by a repulsion,
  with non isolated equilibria I: the regular case.
  SIAM Journal on Control and Optimization, 41 (2002), no. 4, 1254--1280.

• [4] A. Cabot, B. Mohammadi, Incomplete sensitivities and cost function reformulation
  leading to multi-criteria investigation of inverse problems.
  Optimal Control Applications and Methods, 24 (2003), no. 2, 73--84.

• [5] A. Cabot, Inertial gradient-like dynamical system controlled by a stabilizing term.
  Journal of Optimization- Theory and Applications, 120 (2004), no. 2, 275--303.

• [6] F. Alvarez, A. Cabot, Steepest descent with curvature dynamical system.
  Journal of Optimization- Theory and Applications, 120 (2004), no. 2, 247--273.

• [7] A. Cabot, The steepest descent dynamical system with control. Applications to constrained minimization.
  Control, Optimisation and Calculus of Variations, 10 (2004), no. 2, 243--258.

• [8] A. Cabot, Bounce law at the corners of convex billiards.
  Nonlinear Analysis, 57 (2004), no. 4, 597--614.

• [9] A. Cabot, Proximal point algorithm controlled by a slowly vanishing term. Applications to hierarchical minimization.
  SIAM Journal on Optimization, 15 (2005), no. 2, 555--572.

• [10] F. Alvarez, A. Cabot, On the asymptotic behavior of a system of steepest descent equations
  coupled by a vanishing mutual repulsion.
  Recent Advances in Optimization (edité par A. Seeger), Lectures Notes in Econom. and Math. Systems,
  Springer-Verlag (2006), 3--17.

• [11] S. Adly, H. Attouch, A. Cabot, Finite time stabilization of nonlinear oscillators subject to dry friction.
  Nonsmooth Mechanics and Analysis (edité par P. Alart, O. Maisonneuve et R.T. Rockafellar),
  Adv. in Math. and Mech., Kluwer (2006), 289--304.

• [12] B. Baji, A. Cabot, An inertial proximal algorithm with dry friction: finite convergence results.
  Set Valued Analysis, 14 (2006), no. 1, 1--23.

• [13] F. Alvarez, A. Cabot, Asymptotic selection of viscosity equilibria of semilinear evolution equations
  by the introduction of a slowly vanishing term.
  Discrete and Continuous Dynamical Systems, 15 (2006), no. 3, 921--938.

• [14] A. Cabot, A. Seeger, Multivalued exponentiation analysis. Part I: Maclaurin exponentials.
  Set Valued Analysis, 14 (2006), no. 4, 347--379.

• [15] A. Cabot, A. Seeger, Multivalued exponentiation analysis. Part II: Recursive exponentials.
  Set Valued Analysis, 14 (2006), no. 4, 381--411.

• [16] A. Cabot, L. Paoli, Asymptotics for some vibro-impact problem with linear dissipation term.
  Journal de Mathématiques Pures et Appliquées, 87 (2007), no. 3, 291--323.

• [17] B. Baji, A. Cabot, J.I. Diaz, Asymptotics for some nonlinear damped wave equation:
  finite time convergence versus exponential decay results.
  Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 24 (2007), no. 6, 1009--1028.

• [18] A. Cabot, Stabilization of oscillators subject to dry friction: finite time convergence versus exponential decay results.
  Transactions of the American Mathematical Society, 360 (2008), no. 1, 103--121.

• [19] A. Cabot, H. Engler, S. Gadat, On the long time behavior of second order differential equations
  with asymptotically small dissipation. Accepté à Transactions of the American Mathematical Society.