Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux. (Strong solutions and asymptotic behaviour for a natural convection problem in porous media)
Considering the natural convection problem in a porous medium enclosed in an impermeable parallelepipedon with isothermal horizontal faces and adiabatic lateral faces, the author proves by a fixed point method the existence and uniqueness of the strong solutions of the Darcy-Boussinesq equations. We have to mention that, by a different method, the general case has been solved [see the reviewer, On the existence and uniqueness of instationary convection in porous media, An. Stiint. Univ. Al. I. Cuza. Iasi, N. Ser., Sect. Ia 32, No.3, 75-84 (1986)]. In the second part of the article, using a method from the theory of the Navier-Stokes equations, it is proved that the solution is completely determined by its nodal values on a finite set.
scientific article; zbMATH DE number 3986926
scientific article