AI 中文总结
研究一维非局部非线性程函方程，提出半显式（IMEX）格式用于数值逼近，证明该格式保持离散梯度熵估计并在粘性意义下收敛，给出数值结果展示模型行为和格式性能。
AI 中文摘要
在本文中，我们研究了一个一维非局部非线性程函方程，其空间梯度无符号限制。该方程的特征在于非局部速度场和初始数据都具有弱正则性假设。我们推导了此模型的周期形式，并提出了一种半显式（IMEX）格式用于其数值逼近。我们证明该格式保持离散梯度熵估计，并在粘性意义下建立其收敛性。最后，我们给出数值结果来说明模型的行为和所提格式的性能。
英文摘要
In this work, we study a one-dimensional nonlocal and nonlinear eikonal equation without sign restriction on its spatial gradient. The equation is characterized by weak regularity assumptions on both the nonlocal velocity field and the initial data. We derive a periodic version of this model and propose a semi-explicit (IMEX) scheme for its numerical approximation. We prove that the scheme preserves a discrete gradient entropy estimate and establish its convergence in the viscosity sense. Finally, we present numerical results illustrating the behavior of the model and the performance of the proposed scheme.
