Large-time asymptotic stability of Riemann shocks of scalar balance laws

Abstract

We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first order scalar hyperbolic balance laws, under piecewise regular perturbations provided that the source term is dissipative about endstates of the shock. Moreover the convergence towards a shifted reference state is exponential with a rate predicted by the linearized equations about constant endstates.

Added section on transverse stability in the multidimensional framework

References in corpus (1)

• Spectral Stability of Inviscid Roll Waves

Cited by in corpus (3)

• Stability and instability in scalar balance laws: fronts and periodic waves
• Asymptotic stability of viscous shocks in the modular Burgers equation
• Majda and ZND models for detonation: nonlinear stability vs. formation of singularities