Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909686699130880 |
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| author | Arceci, Francesca De Vecchi, Francesco Carlo Morale, Daniela Ugolini, Stefania |
| author_facet | Arceci, Francesca De Vecchi, Francesco Carlo Morale, Daniela Ugolini, Stefania |
| contents | A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum random system is established. A splitting strategy allows us to decompose the random system into a space-discrete heat equation with a stochastic boundary condition, and a nonlinear and nonlocal space-discrete differential system coupled with the first one and with deterministic initial and boundary conditions. The convergence result is obtained by first establishing some a priori estimates for both space-discrete splitted variables and then exploiting compact embedding theorems for time-space Besov spaces on the positive lattice. The convergence of a fully discrete approximation of the random system is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results Arceci, Francesca De Vecchi, Francesco Carlo Morale, Daniela Ugolini, Stefania Probability Numerical Analysis 60H35, 65M06, 65M12 A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum random system is established. A splitting strategy allows us to decompose the random system into a space-discrete heat equation with a stochastic boundary condition, and a nonlinear and nonlocal space-discrete differential system coupled with the first one and with deterministic initial and boundary conditions. The convergence result is obtained by first establishing some a priori estimates for both space-discrete splitted variables and then exploiting compact embedding theorems for time-space Besov spaces on the positive lattice. The convergence of a fully discrete approximation of the random system is also discussed. |
| title | Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results |
| topic | Probability Numerical Analysis 60H35, 65M06, 65M12 |
| url | https://arxiv.org/abs/2507.09278 |