Issue |
ESAIM: COCV
Volume 11, Number 4, October 2005
|
|
---|---|---|
Page(s) | 522 - 541 | |
DOI | https://doi.org/10.1051/cocv:2005021 | |
Published online | 15 September 2005 |
On ergodic problem for Hamilton-Jacobi-Isaacs equations
SISSA/ISAS via Beirut, 2-4 - 34013 Trieste, Italy; bettiol@ma.sissa.it
Received:
20
January
2004
Revised:
3
November
2004
We study the asymptotic behavior of as
, where
is the viscosity solution of the following Hamilton-Jacobi-Isaacs
equation (infinite horizon case)
with
We discuss the cases in which the state of the system is required to stay in an
n-dimensional torus, called periodic boundary conditions,
or in the closure
of a bounded connected domain
with sufficiently smooth boundary.
As far as the latter is concerned, we treat
both
the case of the Neumann boundary conditions
(reflection on the boundary) and
the case of state constraints boundary conditions.
Under the uniform approximate controllability
assumption of one player, we extend
the uniform convergence result of the value function to a constant as
to differential games.
As far as state constraints boundary conditions are concerned,
we give an example where the value function is Hölder continuous.
Mathematics Subject Classification: 35B40 / 49L25 / 49N70
Key words: Hamilton-Jacobi-Isaacs equations / viscosity solutions / asymptotic behavior / differential games / boundary conditions / ergodicity.
© EDP Sciences, SMAI, 2005
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