Energy methods for Cauchy problems of evolutions equations

Stéphane Andrieux (1) , Thouraya Baranger (2)

1 LAMSID - UMR 8193 - Laboratoire de Mécanique des Structures Industrielles Durables
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

In the present paper a numerical method based on minimizing energy functionals, is developed for solving Cauchy problem of evolution equations. Two cases are treated: the parabolic equations as the heat equations and the hyperbolic ones as the elastodynamics equations. The method is first presented in some details, then, illustrated on various applications.

Domaines: Mécanique [physics.med-ph]; Equations aux dérivées partielles [math.AP]; Mécanique des solides [physics.class-ph]; Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Optimisation et contrôle [math.OC]; Génie mécanique [physics.class-ph]; Génie mécanique [physics.class-ph]; Thermique [physics.class-ph]; Thermique [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]

Stéphane Andrieux, Thouraya Baranger. Energy methods for Cauchy problems of evolutions equations. Journal of Physics: Conference Series, 2008, 135, pp.1-9. ⟨10.1088/1742-6596/135/1/012007⟩. ⟨hal-00489551⟩