\(L^{2}\) formulation of multidimensional scalar conservation laws (Q834760)
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| English | \(L^{2}\) formulation of multidimensional scalar conservation laws |
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\(L^{2}\) formulation of multidimensional scalar conservation laws (English)
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27 August 2009
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This paper proposes that \(L^2\) can be a suitable space for entropy solutions to multidimensional scalar conservation laws, provided a different formulation is used, based on a combination of level set, and kinetic and transport-collapse approximations. It is claimed that any Kruzkov solution with initial data in \(L^\infty\) can be recovered up to a trivial rescaling.
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entropy solutions
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level set method
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transport-collapse approximations
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