On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory

Abstract:

The aim of present paper is the demonstration of a method of generalized solutions representation for some quasilinear equations and systems of hyperbolic type. This method is a variational principle of Lax-Oleinik type for one equation and for certain non-strictly hyperbolic systems. But the novelty of proposed approach lies in the fact that the method of construction is totally fifferent from the previous ones. Namely the theory of potential equilibrium in external field is used. This allows constructing the variational representation for generalized solutions of strict hyperbolic systems in non-divergent form

Publication language:english

Research direction:

Mathematical problems and theory of numerical methods