0%

Hamilton Jacobi Equations

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. Hamilton-Jacobi Equations: Theory and Applications [M]