On the existence, uniqueness and stability of entropy solutions to scalar conservation laws

DOI10.1016/j.jde.2012.04.024zbMath1251.35038OpenAlexW1996069996MaRDI QIDQ439105

Publication date: 1 August 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2012.04.024

zbMATH Keywords

Cauchy problem contraction principle entropy solutions existence and uniqueness continuous dependence scalar conservation laws

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Quasilinear parabolic equations (35K59)

Related Items (1)

One-Dimensional Pressureless Gas Systems with/without Viscosity

Cites Work

A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux
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Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems
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Uniqueness of entropy solutions for nonlinear degenerate parabolic problems
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On vanishing viscosity approximation of conservation laws with discontinuous flux
\(L^1\)-theory of scalar conservation law with continuous flux function
A note on uniqueness of entropy solutions to degenerate parabolic equations in \({\mathbb{R}^N}\)
Continuous dependence of the entropy solution of general parabolic equation
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
Pressureless Euler/Euler–Poisson Systems via Adhesion Dynamics and Scalar Conservation Laws
Sticky Particles and Scalar Conservation Laws
On generalized entropy solutions of the Cauchy problem for a first-order quasilinear equation in the class of locally summable functions
Discontinuous solutions of non-linear differential equations
Front tracking for hyperbolic conservation laws
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