Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems
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| Format: | Preprint |
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2025
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| _version_ | 1866910907413561344 |
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| author | Heinze, Georg Mielke, Alexander Stephan, Artur |
| author_facet | Heinze, Georg Mielke, Alexander Stephan, Artur |
| contents | We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete processes and show convergence not only on the level of solutions, but also on the level of the gradient systems governing the evolutions. As an important step, we prove chain rule inequalities for the reaction-diffusion systems as well as their discretizations, featuring a non-convex dissipation functional. The convergence is then obtained with variational methods by building on the recently introduced notion of gradient systems in continuity equation format. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems Heinze, Georg Mielke, Alexander Stephan, Artur Analysis of PDEs Numerical Analysis Mathematical Physics Dynamical Systems 35A15, 35K57, 35A35, 47J35, 65M08 We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete processes and show convergence not only on the level of solutions, but also on the level of the gradient systems governing the evolutions. As an important step, we prove chain rule inequalities for the reaction-diffusion systems as well as their discretizations, featuring a non-convex dissipation functional. The convergence is then obtained with variational methods by building on the recently introduced notion of gradient systems in continuity equation format. |
| title | Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics Dynamical Systems 35A15, 35K57, 35A35, 47J35, 65M08 |
| url | https://arxiv.org/abs/2504.06837 |