Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control   Problem
  We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence, uniqueness and regularity of the optimal solution. Here we obtain the first necessary optimality conditions. 
Moulay Rchid Sidi Ammi, Delfim F. M. Torres