Variational methods as the most effective mechanism for modeling physical interrelated fields in continuous medium. II. Case study

A number of examples, both trivial and complex enough, to demonstrate the effectiveness of variational methods for mathematical modeling of various physical processes. Some of the examples may be modeled using alternative approaches, such as the acoustic model of porous media (Bio theory), probably only modeled using variational techniques. The focus of the review is made on the details cast of the application of variational approach, which is not always done in the original papers in which these methods are used to solve complex problems. In the appendix provides some useful information on variational methods, including the Onsager principle of symmetry of kinetic coefficients and generalized variational principle.