2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131148We 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. Existence and regularity of the optimal solutions for this system is established.Accepted for publication in the journal "Differential Geometry -- Dynamical Systems" (22-July-2006)Optimization and ControlAnalysis of PDEs49J20; 35K55text