Hamilton Jacobi and Chip Manufacture
HAMILTON - JACOBI EQUATION
Models Etching and Deposition
Unique Viscosity Solution: Crandall - Lions
n = 1, Curves in the plane: Complete Theory: Lax-Oleinik.
Closed Form Solutions: when H or U_0 Convex
RIEMANN - PROBLEMS:
Key to Front Tracking Algorithm.
Propagation of Geometric Singularities, Namely Conical Initial Data:
Proposition
RIEMANN PROBLEM:
Given
Riemann Data
Z
Construct
Riemann Solution
U
.
REDUCED HAMILTON - JACOBI EQUATION
Equation for
U
, with v =x/t
VISCOSITY SOLUTION:
DIFFERENTIALS:
Set of Super(Sub)differentials Closed, Convex, Possibly Empty
PARABOLIC SET
EXAMPLE: CVD, 2D
EXAMPLE: NON ISOTROPIC, 2D
ELEMENTARY WAVES
GENERAL RIEMANN PROBLEM
