A variational representation of generalized solutions to quasi-linear hyperbolic systems and possible algorithms for hybrid supercomputers

In the present work the new approach to the study of quasi-linear hyperbolic systems is formulated. This approach is based on the representation of generalized solutions as the set of functions on certain families of curves. Such functions and curves (which occur to be characteristics) are found as the solutions of some variational problem. As a consequence the problem of finding of generalized solutions can be formulated as a set of independent variational problems. The situation highlights the way to possible robust algorithm for calculations with the aid of hybrid supercomputers. The work is written at “physical” level of rigor.