Modelarea suprafeței de rotație cu arie minimă cu aplicație în sisteme de mediu

An analysis is presented for the classical variational problem of determining the shape of a surface of revolution with minimal area. The optimized functional attains a local minimum for all solutions obtained by solving the corresponding Euler equation. The properties and mathematical models of catenoids are relevant in various areas of environmental research, particularly those involving fluid interfaces, surface tension, and porous media. Their properties can therefore be applied to specialized problems related to surface tension, fluid interfaces, nanostructured pollutants, and porous media research. Additionally, catenoids serve as idealized models in computational simulations involving minimal energy configurations in environmental systems.