Analysis of a One-Dimensional Model for Compressible Miscible Displacement in Porous Media

Global BV solutions for a model of multi-species mixture in porous media

“…Section 3 is devoted to the regularization of the problem. Some similar results to those of [2] will be used without proof. In Section 4, we introducé an intermediary variable v and establish its BV estimate.…”

“…The proof of this lemma is analogous to that of [2], we refer the reader to that paper. LEMMA We easily see that, as Ô tends to 0, w converges in H l (Q T ) n weakly to w given by…”

“…This solution is obtained by a compensated compactness argument applied to the approximate solution constructed by the viscosity method [4]- [5]. By the same technique, they also treated some homogenization problems in one space dimension [3]. All these results have been generalized by Amirat-Peng [6], to the case of n + 1 species mixture for which the concentration variables satisfy a hyperbolic system of n équations.…”

“…For this reason, we suppose throughout this paper that z é ^ Zj for ail i ^ j, Our objective is to construct a global weak solution such that the concentration variables are bounded with bounded total variation. In the case n= 1, this resuit has been obtained by Anürat-Moussaoui [2]. Hère we assume that there exists a fonction p e L 2 ( 0, The remainder of the paper deals with the proof of this theorem, the main steps of which is analogous to that of the scalar case n = 1, see [2].…”

“…In the case n= 1, this resuit has been obtained by Anürat-Moussaoui [2]. Hère we assume that there exists a fonction p e L 2 ( 0, The remainder of the paper deals with the proof of this theorem, the main steps of which is analogous to that of the scalar case n = 1, see [2]. In the next section» we introducé a change of variables which is essential to treat the BV estimâtes.…”