16 , 2018-02-02 , Department of Mathematics, Hokkaido University
In the classical level set method, the slope of solutions can be very small or large, and it can make it diﬃcult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper- and lower bound near the zero level set for the viscosity solution to the initial value problem.