6 papers
Orbital stability of monostable waves for reaction-diffusion systems
Louis Garénaux
We study stability of monostable waves for reaction-diffusion systems. When the solution is initially close to a fast wave profile in optimal topology, we prove convergence to a sh…
Orbital stability of plane waves in the Klein-Gordon equation against localized perturbations
Emile Bukieda, Louis Garénaux, Björn de Rijk
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render…
Linear convective stability of a front superposition with unstable connecting state
Louis Garénaux, Bastian Hilder
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction…
Existence of monostable fronts for a KPP infinite-difference numerical scheme
Louis Garénaux, Hermen Jan Hupkes
We study the existence of traveling wave solutions for a numerical counterpart of the KPP equation. We obtain the existence of monostable fronts for all super-critical speeds in th…
Long-time behavior of small solutions in the viscoelastic Klein-Gordon equation
Louis Garénaux, Björn de Rijk
We investigate the long-time behavior of solutions with small initial data to the viscoelastic Klein-Gordon equation with general smooth nonlinearity. Our analysis relies on the sp…
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…