Relative entropy and L2 stability to a shock for scalar balance laws

Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Cites Work

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Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-$BV$ perturbations
$L ^{2}$ stability estimates for shock solutions of scalar conservation laws using the relative entropy method
Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
The second law of thermodynamics and stability
The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
Convergence of solutions to the Boltzmann equation in the incompressible Euler limit
Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics
Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
From discrete velocity Boltzmann equations to gas dynamics before shocks
Relative entropy in hyperbolic relaxation
Scalar conservation laws with general boundary condition and continuous flux function
Strong traces for solutions to scalar conservation laws with general flux
Relative Entropy in Diffusive Relaxation
Relative entropy and contraction for extremal shocks of conservation laws up to a shift
Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
From the BGK model to the Navier–Stokes equations
From the Boltzmann equation to the Stokes-Fourier system in a bounded domain
Asymptotic limit to a shock for BGK models using relative entropy method
From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks
From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II
Strong traces for solutions of multidimensional scalar conservation laws

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