Rayleigh–Type Renormalized Flows in Weighted Geometries Energy Dissipation, Invariance, and Applications to PDE Dynamics
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2025
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| _version_ | 1866901953790869504 |
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| author | Rodrigues de Maria, Mateus |
| author_facet | Rodrigues de Maria, Mateus |
| contents | <p>We introduce a class of Rayleigh–type normalized flows associated with weighted geometries and non–uniform density structures. The dynamics is generated by a weighted Dirichlet operator Aκ = D∗κDκ on L 2 (dµ), where dµ = w dx and Dκ is the renormalized derivative induced by a strictly positive weight w = κ + 1. The flow preserves the L 2 (dµ) constraint and dissipates the Rayleigh energy. We establish invariance and positivity properties, derive a sharp Lyapunov dissipation identity, and characterize stationary states as eigenfunctions of Aκ. We also discuss localization tools and connections with weighted diffusion and PDE avatars.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18061235 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Rayleigh–Type Renormalized Flows in Weighted Geometries Energy Dissipation, Invariance, and Applications to PDE Dynamics Rodrigues de Maria, Mateus Rayleigh flow constrained gradient dynamics weighted Dirichlet forms energy dissipation eigenmode selection <p>We introduce a class of Rayleigh–type normalized flows associated with weighted geometries and non–uniform density structures. The dynamics is generated by a weighted Dirichlet operator Aκ = D∗κDκ on L 2 (dµ), where dµ = w dx and Dκ is the renormalized derivative induced by a strictly positive weight w = κ + 1. The flow preserves the L 2 (dµ) constraint and dissipates the Rayleigh energy. We establish invariance and positivity properties, derive a sharp Lyapunov dissipation identity, and characterize stationary states as eigenfunctions of Aκ. We also discuss localization tools and connections with weighted diffusion and PDE avatars.</p> |
| title | Rayleigh–Type Renormalized Flows in Weighted Geometries Energy Dissipation, Invariance, and Applications to PDE Dynamics |
| topic | Rayleigh flow constrained gradient dynamics weighted Dirichlet forms energy dissipation eigenmode selection |
| url | https://doi.org/10.5281/zenodo.18061235 |