Year: 2025
Type: preprint
Abstract: We study the vanishing viscosity method for the eikonal equation $|Du|=V$ in $B(0,1)$ with homogeneous Dirichlet boundary value condition. By assuming $V$ is radially symmetric and restricting attention to radially symmetric solutions, we construct explicit formulas for both the viscous solution $u^ε$ and the limiting solution $u$. We prove $u^ε\rightarrow u$ as $ε\rightarrow 0^+$ qualitatively and quantitatively derive an $ε|\log ε|$ type local convergence rate. Finally, we discuss the uniqueness of viscosity solutions for the eikonal equation and give some examples.
Source: arXiv (Cornell University)
Author: Meng, Fanchen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414536837
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