2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139871We 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.9 pagesOptimization and ControlAnalysis of PDEs49K20; 35K55text