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math.AP2026★ 1 cited
Existence and behavior of steady solutions on an interval for general hyperbolic-parabolic systems of conservation laws
Benjamin Melinand, Kevin Zumbrun
We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservatio…
math.AP2024
Rigid Lid limit in shallow water over a flat bottom
Benjamin Melinand
We perform the so-called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green-Naghdi equations. To do so we consider an appropriate n…
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…