Dynamics of discrete random Burgers-Huxley systems: attractor convergence and finite-dimensional approximations

Fuente: arXiv
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Autores principales: Su, Fang, Wang, Xue
Formato: Preprint
Publicado: 2025
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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