Study of an industrial chemical tubular continuous reactor led to a nonclassical distributed parameter model involving a boundary point whose position is time-dependent and an implicit limit condition. This is due to a phase changing phenomenon (evaporation) within the reactor which occurs at a precise point for a given time. This paper deals with a method of solving the hyperbolic partial differential equations with Dirichlet-type limit conditions, one of them being implicit and time-dependent. Then a control model is proposed, keeping this physical aspect in its structure. This control model is used with a finite-dimensional multivariable optimal control law, both in a simulation and in applications to an industrial reactor. The results allow the proposed methods to be generalized for similar chemical or physical processes.