Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917801917153280 |
|---|---|
| author | Elgrou, Abdellatif Maniar, Lahcen Oukdach, Omar |
| author_facet | Elgrou, Abdellatif Maniar, Lahcen Oukdach, Omar |
| contents | In this paper, we study a multi-objective inverse initial problem with a Nash strategy constraint for forward stochastic reaction-diffusion equations with dynamic boundary conditions, where both the volume and surface equations are influenced by randomness. The objective is twofold: first, we maintain the state close to prescribed targets in fixed regions using two controls; second, we determine the history of the solution from observations at the final time. To achieve this, we establish new Carleman estimates for forward and backward equations, which are used to prove an interpolation inequality for a coupled forward-backward stochastic system. Consequently, we obtain two results: backward uniqueness and a conditional stability estimate for the initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions Elgrou, Abdellatif Maniar, Lahcen Oukdach, Omar Analysis of PDEs In this paper, we study a multi-objective inverse initial problem with a Nash strategy constraint for forward stochastic reaction-diffusion equations with dynamic boundary conditions, where both the volume and surface equations are influenced by randomness. The objective is twofold: first, we maintain the state close to prescribed targets in fixed regions using two controls; second, we determine the history of the solution from observations at the final time. To achieve this, we establish new Carleman estimates for forward and backward equations, which are used to prove an interpolation inequality for a coupled forward-backward stochastic system. Consequently, we obtain two results: backward uniqueness and a conditional stability estimate for the initial conditions. |
| title | Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.10007 |