L formulation of multidimensional scalar conservation laws

Se p 20 06 L 2 formulation of multidimensional scalar conservation laws

AMS classification : 35L65, 47H05 Abstract We show that Kruzhkov’s theory of entropy solutions to multidimensional scalar conservation laws [Kr] can be entirely recast in L 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, M...

L2 formulation of multidimensional scalar conservation laws

Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws

Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L–stability. New multidimensional features are recognized, especially including nonlinear propagations of oscilla...

A Kinetic Formulation for Multidimensional Scalar Conservation Laws with Boundary Conditions and Applications

Well-posedness for Multidimensional Scalar Conservation Laws with Discontinuous Flux

We obtain a well-posedness result of an entropy solution to a multidimensional scalar conservation law with discontinuous (quasi-homogeneous) flux satisfying crossing conditions, but with no genuine nonlinearity assumptions. The proof is based on the kinetic formulation of the equation under consideration and it does not involve any transformation of the original equation or existence of strong...