Dynamics of discrete random Burgers-Huxley systems: attractor convergence and finite-dimensional approximations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908304264921088 |
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| author | Su, Fang Wang, Xue |
| author_facet | Su, Fang Wang, Xue |
| contents | In this paper, we apply the implicit Euler scheme to discretize the (random) Burgers-Huxley equation and prove the existence of a numerical attractor for the discrete Burgers-Huxley system. We establish upper semi-convergence of the numerical attractor to the global attractor as the step size tends to zero. We also provide finite-dimensional approximations for the three attractors (global, numerical and random) and prove the existence of truncated attractors as the state space dimension goes to infinity. Finally, we prove the existence of a random attractor and establish that the truncated random attractor upper semi-converges to the truncated global attractor as the noise intensity tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of discrete random Burgers-Huxley systems: attractor convergence and finite-dimensional approximations Su, Fang Wang, Xue Analysis of PDEs 34D45, 37K60, 65L20 In this paper, we apply the implicit Euler scheme to discretize the (random) Burgers-Huxley equation and prove the existence of a numerical attractor for the discrete Burgers-Huxley system. We establish upper semi-convergence of the numerical attractor to the global attractor as the step size tends to zero. We also provide finite-dimensional approximations for the three attractors (global, numerical and random) and prove the existence of truncated attractors as the state space dimension goes to infinity. Finally, we prove the existence of a random attractor and establish that the truncated random attractor upper semi-converges to the truncated global attractor as the noise intensity tends to zero. |
| title | Dynamics of discrete random Burgers-Huxley systems: attractor convergence and finite-dimensional approximations |
| topic | Analysis of PDEs 34D45, 37K60, 65L20 |
| url | https://arxiv.org/abs/2504.04426 |