On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917271759224832 |
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| author | Belin, Théo Schneider, Guido |
| author_facet | Belin, Théo Schneider, Guido |
| contents | We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems and relies on key maximal regularity results. The theorem is applied to the Gray-Scott-Klausmeier vegetation-water interaction model and its application to general reaction-diffusion-advection systems is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems Belin, Théo Schneider, Guido Analysis of PDEs Dynamical Systems (Primary) 35B40, (Secondary) 35B32, 35B36, 35K59 We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems and relies on key maximal regularity results. The theorem is applied to the Gray-Scott-Klausmeier vegetation-water interaction model and its application to general reaction-diffusion-advection systems is discussed. |
| title | On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems |
| topic | Analysis of PDEs Dynamical Systems (Primary) 35B40, (Secondary) 35B32, 35B36, 35K59 |
| url | https://arxiv.org/abs/2601.16145 |