Events
DMS Applied and Computational Mathematics Seminar |
| Time: Apr 20, 2026 (03:00 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Son Tu (Baylor University)
Title: Vanishing Viscosity for Hamilton–Jacobi Equations and Applications to Operator Splitting
Abstract: In this talk, I will discuss recent developments on the vanishing viscosity problem for Hamilton–Jacobi equations. After briefly reviewing the historical background and recent progress, I will present an application to error estimates for an operator-splitting method for second-order Hamilton–Jacobi equations. The scheme decomposes the equation into a heat step and a purely first-order step. The first-order part is implemented using a gradient-value policy iteration algorithm, enabling efficient characteristic-based machine learning methods.
We show that the sup-norm error is bounded below by O(h) and above by O(h^1/5) for Lipschitz initial data, improving to O(h^1/3) for semiconcave data, where h is the splitting step. In the periodic setting, the lower L1 bound error is O(h), and the upper bound L1 error is O(h^1/2).
This is joint work with Alain Bensoussan, Thien P. B. Nguyen, and Minh-Binh Tran.
Host: Yuming Paul Zhang
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