Education 2005 Qualification to the Maˆıtre de conférences position (French University position), section 26-Mathématiques appliquées et applications des mathématiques.
This work is focused on the dissipative system ∂ tt u + ∂ xxxx u + ∂ xx θ − β + ∂ x u 2 L 2 (0,1) ∂ xx u = f ∂ t θ − ∂ xx θ − ∂ xxt u = g describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of θ. Under natural boundary conditions, we prove the existence of… (More)
The phase-field model is applied to describe phase transitions which occur in a finite or unbounded region rather than at a sharp surface. The order parameter, or phase field ϕ, is then allowed to vary smoothly within the pertinent region between two extreme values: ϕ = 0, the less ordered phase, and ϕ = 1, the more ordered one. The literature on the… (More)
In this paper we study the gauge-invariance of the time-dependent Ginzburg Landau equations through the introduction of a model which uses observable variables. Since different choices of gauge lead to a different representation of such variables, the classical formulations of the Ginzburg Landau model do not allow to establish the property of… (More)