TY - JOUR T1 - Lagrangian representations for linear and nonlinear transport JF - Contemporary Mathematics. Fundamental Directions Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - Elio Marconi AB -

In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

PB - Peoples' Friendship University of Russia VL - 63 UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng ER -