Riv. Mat. Univ. Parma, Vol. 3, No. 1, 2012

Daniela Tonon

Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to Convection Theory and sticky particles

Pages: 163-175
Received: 7 October 2010   
Accepted: 17 December 2010
Mathematics Subject Classification (2000): 35L65, 35D10, 35Q35.

Keywords: SBV regularity, pressureless gasses, sticky particles, Convection Theory, Generalized Hydrostatic Boussinesq equations, Hamilton-Jacobi equations, scalar conservation laws.

Abstract: We show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.


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