Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918013685465088 |
|---|---|
| author | Maurelli, Mario Morale, Daniela Ugolini, Stefania |
| author_facet | Maurelli, Mario Morale, Daniela Ugolini, Stefania |
| contents | We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical reaction of sulphur dioxide with calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a stochastic differential equation with a mean-reverting drift and a bounded diffusion coefficient. The main result is the global existence and the pathwise uniqueness of mild solutions. The proof relies on a splitting strategy, which allows to deal with the low regularity of the dynamical boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06847 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions Maurelli, Mario Morale, Daniela Ugolini, Stefania Probability Analysis of PDEs 35R60, 60H15, 35K57, 60H30 We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical reaction of sulphur dioxide with calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a stochastic differential equation with a mean-reverting drift and a bounded diffusion coefficient. The main result is the global existence and the pathwise uniqueness of mild solutions. The proof relies on a splitting strategy, which allows to deal with the low regularity of the dynamical boundary condition. |
| title | Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions |
| topic | Probability Analysis of PDEs 35R60, 60H15, 35K57, 60H30 |
| url | https://arxiv.org/abs/2308.06847 |