PHASE SINKS AND SOURCES AROUND TWO-DIMENSIONAL PERIODIC-WAVE SOLUTIONS OF REACTION-DIFFUSION-ADVECTION SYSTEMS - Université Paris Dauphine
Pré-Publication, Document De Travail Année : 2024

PHASE SINKS AND SOURCES AROUND TWO-DIMENSIONAL PERIODIC-WAVE SOLUTIONS OF REACTION-DIFFUSION-ADVECTION SYSTEMS

Résumé

We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide a sharp asymptotic description of the dynamics resulting from both localized and critically nonlocalized perturbations. In particular, we show that the long-time behavior is governed at leading order by a second-order Whitham modulation system and elucidate how the intertwining of diffusive and dispersive effects may enhance decay rates. The latter requires a non trivial extension of the large-time estimates for constant-coefficient hyperbolicparabolic operators to some classes of systems with no particular structure, including on one hand systems with a scalar-like -but not scalar -hyperbolic part and a cross-diffusion, and on the other hand anisotropic systems with dispersion.
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Dates et versions

hal-04679839 , version 1 (28-08-2024)

Identifiants

Citer

Benjamin Melinand, L. Miguel Rodrigues. PHASE SINKS AND SOURCES AROUND TWO-DIMENSIONAL PERIODIC-WAVE SOLUTIONS OF REACTION-DIFFUSION-ADVECTION SYSTEMS. 2024. ⟨hal-04679839⟩
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