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Quantitative stochastic homogenization of an unbounded front propagation problem
Mathematical Models and Methods in Applied Sciences ( IF 3.6 ) Pub Date : 2022-09-27 , DOI: 10.1142/s0218202522500439
Ahmed Hajej 1
Affiliation  

We obtain quantitative stochastic homogenization results for Hamilton–Jacobi equations arising in front propagation problems which move in the normal direction with a possible unbounded velocity. More precisely, we establish error estimates and rates of convergence for homogenization and effective Hamiltonian. The main idea is to perturb our unbounded problem by a bounded one, and to establish stability results in this context. Then, we combine the estimates that we find with the ones from the bounded case.



中文翻译:

无界前向传播问题的定量随机同质化

我们获得了在前向传播问题中出现的 Hamilton-Jacobi 方程的定量随机均匀化结果,这些前向传播问题以可能的无界速度沿法线方向移动。更准确地说,我们为同质化和有效哈密顿量建立了误差估计和收敛速度。主要思想是通过一个有界问题来扰乱我们的无界问题,并在这种情况下建立稳定性结果。然后,我们将我们找到的估计与有界情况的估计结合起来。

更新日期:2022-09-27
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