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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20453 |
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| _version_ | 1866913000190902272 |
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| author | Hoang, The Tuan Tham, Nhu Phong Tang, Bao Quoc |
| author_facet | Hoang, The Tuan Tham, Nhu Phong Tang, Bao Quoc |
| contents | The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel $Ω$ and the other chemical lies only on the boundary $\partialΩ$ where the reaction takes place. In the limit as the reaction rate constant tends to infinity, we prove that the solution converges in $L^p(0,T;L^p(Ω))$ to the solution of a heat equation with nonlinear dynamical boundary condition. This is obtained by showing a-priori estimates of solutions which are uniform in the reaction rate constants. In order to overcome the difficulty caused by the bulk-surface coupling, we consider the limit in suitable product spaces where the Aubin-Lions lemma is applicable. Moreover, in the case of equal stoichiometric coefficients, we obtain the convergence rate of the fast reaction limit by exploiting suitable estimates of the limiting system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20453 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast reaction limits and convergence rate for nonlinear bulk-surface reaction-diffusion systems modeling reversible chemical reactions Hoang, The Tuan Tham, Nhu Phong Tang, Bao Quoc Analysis of PDEs The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel $Ω$ and the other chemical lies only on the boundary $\partialΩ$ where the reaction takes place. In the limit as the reaction rate constant tends to infinity, we prove that the solution converges in $L^p(0,T;L^p(Ω))$ to the solution of a heat equation with nonlinear dynamical boundary condition. This is obtained by showing a-priori estimates of solutions which are uniform in the reaction rate constants. In order to overcome the difficulty caused by the bulk-surface coupling, we consider the limit in suitable product spaces where the Aubin-Lions lemma is applicable. Moreover, in the case of equal stoichiometric coefficients, we obtain the convergence rate of the fast reaction limit by exploiting suitable estimates of the limiting system. |
| title | Fast reaction limits and convergence rate for nonlinear bulk-surface reaction-diffusion systems modeling reversible chemical reactions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.20453 |