22 citations · 22 across the 5 of their papers we have counts for
5 papers
Nonlinear stability of two-dimensional periodic waves in parabolic systems with conservation laws
L. Miguel Rodrigues, Aric Wheeler
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusiv…
Small-amplitude finite-depth Stokes waves are transversally unstable
Ziang Jiao, L. Miguel Rodrigues, Changzhen Sun +1
We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravi…
Convective stability in scalar balance laws
Louis Garénaux, L. Miguel Rodrigues
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stab…
Linear Asymptotic Stability and Modulation Behavior near Periodic Waves of the Korteweg-de Vries Equation
L. Miguel Rodrigues
We provide a detailed study of the dynamics obtained by linearizing the Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal wave. In a suitable sense, l…
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
Maxime Herda, Luis Miguel Rodrigues
The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background…