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math.AP2025
Linear damping estimates for periodic roll wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic balance laws
L. Miguel Rodrigues, Kevin Zumbrun
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the invisc…
math.AP2024
Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems
Benjamin Melinand, L. Miguel Rodrigues
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assump…