Hypersurfaces Moving With Curvature-Dependent Speed: Hamilton-Jacobi Equations, Conservation Laws And Numerical Algorithms

this paper is to show that algorithms based on direct parameterizations of the moving front face considerable difficulties. This is because such algorithms adhere to local properties of the solution, rather than the global structure. Conversely, the global properties of the motion can be captured by imbedding the surface in a higher-dimensional function. In this setting, the equations of motion can be solved using numerical techniques borrowed from hyperbolic conservation laws. We use these schemes to follow a variety of propagation problems, illustrating corner formation, breaking and merging. This paper appeared as Sethian, J.A., Journal of Differential Geometry, 31, pp. 131-161, (1989).} This work is supported in part by the Applied Mathematics Subprogram of the Office of Energy Research under contract DE-AC03-76SF00098. The author also acknowledges the support of the National Science Foundation and the Sloan Foundation. Hypersurfaces Moving with Curvature-Dependent Speed: Hamilton-Jacobi Equations, Conservation Laws and Numerical Algorithms J.A. Sethian Department of Mathematics University of California Berkeley, CA. 94720 In many physical problems, interfaces move with speed that depends on the local curvature. Explicit solutions seldom exist. Thus, there is great interest in numerical algorithms that approximate the position of the moving front. The goal of this paper is to show that algorithms based on direct parameterizations of the moving front face considerable difficulties. This is because such algorithms adhere to local properties of the solution, rather than the global structure. Conversely, the global properties of the motion are preserved by imbedding the surface in a higher-dimensional function. In this setting, the resulting equations of motion can be..