L2 formulation of multidimensional scalar conservation laws

Details L2 formulation of multidimensional scalar conservation laws L2 formulation of multidimensional scalar conservation laws

2006-09-27

arxiv.org/abs/math/0609761v1

Mathematics

Analysis of PDEs

Scientific paper

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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