Key result
A new formulation of classical Kruzkov entropy solutions for multidimensional scalar conservation laws established the well-posedness of initial value problems and saturated solutions.
Key points are not available for this paper at this time.
May enhance theoretical modeling in hemodynamics research; leaves open clinical translation and validation.
We revisit the classical theory of multidimensional scalar conservation laws. We reformulate the notion of the classical Kruzkov entropy solutions and study some new properties as well as the well-posedness of the initial value problem with inhomogeneous fluxes and general initial data. We also consider Dirichlet boundary value problems. We put forward a new and transparent definition for solutions and give a simple proof for their well-posedness in domains with smooth boundaries. Finally, we introduce the notion of saturated solutions and show that it is well-posed.
No takes yet. Share an insight, caveat, or question.
Lions et al. (2018) studied this question. A new formulation of classical Kruzkov entropy solutions for multidimensional scalar conservation laws established the well-posedness of initial value problems and saturated solutions.
Synapse has enriched one closely related paper. Consider it for comparative context: