Convexity and Absolute Continuity of the Laplace-Beltrami Operator.
Convexity and uniqueness in a free boundary problem arising in combustion theory.
We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such thatut = Δu, in Ω,u = 0 and |∇u| = 1, on Γ := ∂Ω ∩ QT,u(·,0) = u0, on Ω0,where Ω0 is a given domain in Rn and u0 is a positive and continuous function in Ω0, vanishing on ∂Ω0. If Ω0 is convex and u0 is concave in Ω0, then we show that (u,Ω) is unique and the time sections...
Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis