Gui-Qiang G. Chen

[Submitted on 28 Oct 2024] Title:A New Formula for Entropy Solutions for Scalar Hyperbolic Conservation Laws: Convexity Degeneracy of Flux Functions and Fine Properties of Solutions View a PDF of the paper titled A New Formula for Entropy Solutions for Scalar Hyperbolic Conservation Laws: Convexity Degeneracy of Flux Functions and Fine Properties of Solutions, by Gaowei Cao and 2 other authors View PDF Abstract:We are concerned with the Cauchy problem for one-dimensional scalar hyperbolic...

1 INTRODUCTION ∂ t ρ + div M = 0 , ∂ t M + div ( M ⊗ M ρ ) + ∇ p + ρ ∇ Φ = 0 , Δ Φ = κ ρ , $$\begin{equation} \left\{ \def\eqcellsep{&}\begin{array}{l} {{\partial}_{t}\rho +\text{div}\mathcal{M}=0,}\\[8pt] {\displaystyle {\partial}_{t}\mathcal{M}+\text{div}\Big(\frac{\mathcal{M}\otimes \mathcal{M}}{\rho}\Big)+\nabla p+\rho \nabla \mathrm{\Phi}=\mathbf{0},}\\[3pt] {\mathrm{\Delta}\mathrm{\Phi}=\kappa \rho ,}\end{array} \right.