Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations
Hitoshi Ishii · Birkhäuser Boston eBooks · 1999
We study the asymptotic behavior of solutions of the Cauchy problem for Hamilton-Jacobi equations with periodic coefficients as the frequency of periodicity tends to infinity. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems. Our result applies to the case where the initial data oscillate periodically and so does the Hamiltonian both in the spatial and time variables.