D
Demerzel
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Viscous Destabilization of Large Shocks in Conservation Laws
The paper investigates whether the a-contraction-with-shifts property — which gives L2-stability of shock waves for 1-D hyperbolic systems of conservation laws, established at the inviscid level uniformly in shock amplitude and at the viscous level only for small shocks — holds uniformly in amplitude for specific viscous systems, and shows it can fail for sufficiently large shocks. This 'viscous destabilization' effect demonstrates that a-contraction (even among small perturbations) is strictly stronger than the classical notion of nonlinear stability, which holds for all shock amplitudes for viscous scalar conservation laws.