Sur un problème de type elliptique parabolique non linéaire

We study the general equation b(u)_t=a(u,?(u)_x)_x+f of elliptic-parabolic type. Using the theory of evolution equation governed by accretive operator, we establish existence and uniqueness of mild solutions to the associate Cauchy problem, under general assumptions on the data. With additional structural condition of Alt–Luckhauss type, we show that the mild solutions are weak solutions. To cite this article: S. Ouaro, H. Touré, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 27–30