| Abstract: |
| We discuss a few steps towards a complete stability theory for genuinely multidimensional periodic traveling waves of parabolic systems.
On the one hand for large classes of parabolic systems we prove that spectral stability implies nonlinear asymptotic stability in a suitable sense.
On the other hand, for two-dimensional reaction-diffusion systems we provide large-time asymptotics in terms of solutions to averaged, modulation systems. Thus, for such systems, we extend the comprehensive theory now available for plane periodic waves to the multidimensional context.
Concerning the latter, a significant part of the analysis is devoted to obtaining new results on near-constant anisotropic dynamics, to be applied to the averaged systems and including dispersive-diffusive estimes and derivations of artificial viscosity systems. |
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