Self-similar Expanding Solutions in a Sector for a Crystalline Flow
Mi-Ho Giga, Yoshikazu Giga, Hidekata Hontani · SIAM Journal on Mathematical Analysis · 2005
For a given sector a self-similar expanding solution to a crystalline flow is constructed. The solution is shown to be unique. Because of self-similarity the problem is reduced to solve a system of algebraic equations of degree two. The solution is constructed by a method of continuity and obtained by solving associated ordinary differential equations. The self-similar expanding solution is useful to construct a crystalline flow from an arbitrary polygon not necessarily admissible.