Abstract
Chapter 1
- The definition of the viscosity solution
- The construction of the viscosity solution
- The Comparison Principle
- Priori Estimation
- Finite propagation for Cauchy problems
- Rate of convergence
Hamilton Jacobi equation chpt1
Chapter 2
- Dynamic Programming Principle
- Legendre’s transform
- The Hopf-Lax formula
- First-order front propagation problem
Hamilton Jacobi equation chpt2
Chapter 4
- Periodic Hamiltonian
- The cell problem
- The construction of the effective Hamiltonian
- The properties of the effective Hamiltonian
- The inf-sup formula
- The computation for the effective Hamiltonian
- Rate of convergence
Hamilton Jacobi equation chpt4
Reference: Hung Vinh Tran. Hamliton-Jacobi Equations: Theory and Applications [M]