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| Autori principali: | , , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2408.06177 |
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| _version_ | 1866929456132653056 |
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| author | Morgan, Jeff Soresina, Cinzia Tang, Bao Quoc Tran, Bao-Ngoc |
| author_facet | Morgan, Jeff Soresina, Cinzia Tang, Bao Quoc Tran, Bao-Ngoc |
| contents | We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The model was proposed in [Giannino, Iuorio, Soresina, forthcoming] to account for stable stationary spacial patterns considering only biomass and toxicity, and its fast-reaction (cross-diffusion) limit was formally derived and numerically investigated. In this paper, the cross-diffusion limiting system is rigorously obtained as the fast-reaction limit of the reaction-diffusion system with fast-reaction terms by performing a bootstrap argument involving energies. Then, a thorough well-posedness analysis of the cross-diffusion system is presented, including a $L^\infty_{x,t}$-bound, uniqueness, stability, and regularity of weak solutions. This analysis, in turn, becomes crucial to establish the convergence rate for the fast reaction limit, thanks to the key idea of using an inverse Neumann Laplacian operator. Finally, numerical experiments illustrate the analytical findings on the convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular limit and convergence rate via projection method in a model for plant-growth dynamics with autotoxicity Morgan, Jeff Soresina, Cinzia Tang, Bao Quoc Tran, Bao-Ngoc Analysis of PDEs We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The model was proposed in [Giannino, Iuorio, Soresina, forthcoming] to account for stable stationary spacial patterns considering only biomass and toxicity, and its fast-reaction (cross-diffusion) limit was formally derived and numerically investigated. In this paper, the cross-diffusion limiting system is rigorously obtained as the fast-reaction limit of the reaction-diffusion system with fast-reaction terms by performing a bootstrap argument involving energies. Then, a thorough well-posedness analysis of the cross-diffusion system is presented, including a $L^\infty_{x,t}$-bound, uniqueness, stability, and regularity of weak solutions. This analysis, in turn, becomes crucial to establish the convergence rate for the fast reaction limit, thanks to the key idea of using an inverse Neumann Laplacian operator. Finally, numerical experiments illustrate the analytical findings on the convergence rate. |
| title | Singular limit and convergence rate via projection method in a model for plant-growth dynamics with autotoxicity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.06177 |