Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914925001048064 |
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| author | Melinand, Benjamin Rodrigues, L. Miguel |
| author_facet | Melinand, Benjamin Rodrigues, L. Miguel |
| contents | 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 hyperbolic-parabolic 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems Melinand, Benjamin Rodrigues, L. Miguel Analysis of PDEs 35B35, 35K57, 35C07, 35B40, 35B10, 37L15 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 hyperbolic-parabolic 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. |
| title | Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems |
| topic | Analysis of PDEs 35B35, 35K57, 35C07, 35B40, 35B10, 37L15 |
| url | https://arxiv.org/abs/2408.14869 |