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Preprint 2006-034

L2 formulation of multidimensional scalar conservation laws

Yann Brenier

Abstract: 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.

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Author(s):
Yann Brenier,
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Submitted by:
; 2006-09-27.