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The Aubry-Mather theory to difference Hamilton-Jacobi equations

Hold Date
2010-06-04 14:45〜2010-06-04 15:45
Fukuoka University, Seminar House, room A
Object person
Kohei SOGA (Waseda University)

*関数方程式・力学系 合同セミナーです。

We consider periodically time-dependent Hamiltonian systems with
one degree of freedom, the corresponding Hamilton-Jacobi
equations and scalar conservation laws. The relation among them
is made clear by Albert Fathi and Weinan E. In this talk we focus
our attention on numerical aspects of the issue.  First we see
results of difference approximation of periodic entropy solutions
to the conservation laws and apply them to the computation of the
Aubry-Mather sets. Then we translate the approximation into that
of viscosity solutions of the Hamilton-Jacobi equations and find
Aubry-Mather theory like relation among these approximate
objects. The key tool of our arguments is a stochastic and
variational representation of difference solutions which
corresponds to the variational representation of viscosity
solutions by the value function.