Extremal properties of the functionals connected with the systems of conservation laws

The paper contains a further concretization of the variational approach to the theory of systems of conservation laws described in the earlier author’s work. This approach involves the development of methods for proving the existence and uniqueness theorems for generalized solutions that are based on the search for critical points of functionals in Banach spaces. A new definition of the generalized solution is proposed and its equivalence to the traditional one for the functions of a simple structure is proved. A new strategy for proving existence and uniqueness theorems is proposed. A number of illustrative theorems outlining the implementation of this strategy are proved.