Kaouther Ammar

Existence of renormalized solutions of degenerate elliptic-parabolic problems

We consider a general class of degenerate elliptic-parabolic problems associated with the equation b (υ) t = div a (υ, Dυ ) + f . Existence of renormalized solutions is established for general L 1 data. Uniqueness of renormalized solutions has already been shown in a previous work.

Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A1, A2,] with A1 ≤ 0 ≤ A2 so that the problem is of parabolic-hyperbolic type.

Solutions entropiques des problèmes non locaux

Resume On introduit une notion de solution entropique pour le probleme non local C f+f=ψ sur ∂Ω , ou ψ∈ L 1 (∂Ω) et C est un operateur capacite non lineaire, puis on prouve son existence et unicite. Cette notion de solution permet aussi de resoudre un probleme elliptique general avec conditions au bord non lineaires. Pour citer cet article : K. Ammar, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 751–756.