We consider weak solutions with finite entropy production to the scalar conservation law ∂tu+divxF(u)=0in(0,T)×Rd.Building on the kinetic formulation we prove under suitable nonlinearity assumption on f that the set of non Lebesgue points of u has Hausdorff dimension at most d. A notion of Lagrangian representation for this class of solutions is introduced and this allows for a new interpretation of the entropy dissipation measure.
On the structure of weak solutions to scalar conservation laws with finite entropy production
Marconi E.
2022
Abstract
We consider weak solutions with finite entropy production to the scalar conservation law ∂tu+divxF(u)=0in(0,T)×Rd.Building on the kinetic formulation we prove under suitable nonlinearity assumption on f that the set of non Lebesgue points of u has Hausdorff dimension at most d. A notion of Lagrangian representation for this class of solutions is introduced and this allows for a new interpretation of the entropy dissipation measure.
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