L2 formulation of multidimensional scalar conservation laws

Yann Brenier (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IWD - Institut Wolfgang Döblin

We show that Kruzhkov's theory of entropy solutions to multidimensional scalar conservation laws can be entirely recast in L2 and fits into the general theory of maximal monotone operators in Hilbert spaces. Our approach is based on a combination of level-set, kinetic and transport-collapse approximations, in the spirit of previous works by Giga, Miyakawa, Osher, Tsai and the author.

Mots clés: scalar conservation laws; kinetic approximation; maximal monotone operator; level sets

Domaines: Equations aux dérivées partielles [math.AP]

Yann Brenier. L2 formulation of multidimensional scalar conservation laws. 2006. ⟨hal-00101596⟩