You can download my papers about Hamilton-Jacobi Equation and conservation laws here:
Asymptotic Phases in a Cell Differentiation Model by Avner Friedman, Chiu-Yen Kao, Chih-Wen Shih, In preparation
Cell Cycle Control at the First Restriction Point and its Effect on Tissue Growth by Avner Friedman, Bei Hu and Chiu-Yen Kao, submitted to Journal of Journal of Mathematical Biology
Legendre-Transfrom-Based Fast Sweeping Methods for Static Hamilton-Jacobi Equations on Triangulated Meshes by Chiu Yen Kao, Stanley Osher and Jianliang Qian, Journal of Computational Physics, 227(24), Pages 209-225,2008
Properties of A Level Set Algorithm for the Visibility Problems by by Chiu-Yen Kao and Richard Tsai, UCLA Math CAM Reports 06-04 , Journal of Scientific Computing,35(2), Pages 170-191, 2008
Brain MR Image Segmentation by Minimizing Scalable Neighborhood Intensity Fitting Energy: A Multiphase Level Set Approach by Chunming Li, Li Wang, Chiu-Yen Kao, John C. Gore, and Zhaohua Ding, ISMRM 2008
Incorporating Topological Derivatives into Shape Derivatives Based Level Set Methods by Lin He, Chiu-Yen Kao and Stanley Osher, UCLA Math CAM Report 06-44, Journal of Computational Physics, 225, Pages 891-909,2007
Maximizing Band Gaps in Two Dimensional Photonic Crystals by Using Level Set Methods by Chiu-Yen Kao, Stanley Osher, and Eli Yablonovitch, UCLA Math CAM Reports 05-05, Applied Physics B: Lasers and Optics, 81, Pages 235-244,2005
White Matter Tractography by Anisotropic Wavefront Evolution and Diffusion Tensor Imaging by Marcel Jackowski, Chiu Yen Kao, Maolin Qiu, R. Todd Constable, and Lawrence H. Staib, UCLA Math CAM Reports 05-03, Medical Image Analysis,9, Pages 427-440,2005
The Lax-Friedrichs Sweeping Method for Optimal Control Problems in Continuous and Hybrid Dynamics by Chiu Yen Kao, Carmeliza Navasca, and Stanley Osher, UCLA Math CAM Reports 04-24, Nonlinear Analysis, 63, Pages e1561-e1572,2005
Fast Sweeping Methods for Hamilton-Jacobi Equations by Chiu Yen Kao, Stanley Osher and Yen-His Tsai, UCLA Math CAM Reports 02-66, SIAM Numerical Analysis, 42, Pages 2612-2632,2005
Estimation of Anatomical Connectivity by Anisotropic Front Propagation and Diffusion Tensor imaging by Marcel Jackowski, Chiu Yen Kao, Maolin Qiu, R. Todd Constable, and Lawrence H. Staib, UUCLA Math CAM Reports 04-08, MICCAI (2) 2004: Pages 663-670
Lax-Friedrichs Sweeping Scheme for Static Hamilton-Jacobi Equations by Chiu Yen Kao, Stanley Osher and Jianliang Qian, UCLA Math CAM Report 03-38, Journal of Computational Physics,196(1), Pages 367-391,2004