A mathematical model is the representation, through equations, of the phenomenon that you want to model. In the context of control systems, models are used to analyze and design control systems. A system is dynamic when its variables change depending on another variable, which is generally time. In this article, an absorption refrigeration system is considered, a model and simulation of it is carried out and the results are compared with the available experimental data, where the existence and uniqueness of the solution in a certain space of finite smoothness is demonstrated, and the certain properties of the solution to the problem.