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.
Lagrangian Representations for Linear and Nonlinear Transport / Bianchini, S.; Bonicatto, P.; Marconi, E.. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - 253:5(2021), pp. 642-659. (Intervento presentato al convegno Special semester at Harvard tenutosi a Boston, US nel April-May 2016) [10.1007/s10958-021-05259-9].
Lagrangian Representations for Linear and Nonlinear Transport
Bianchini S.;Bonicatto P.;
2021-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
