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MSRI Summer Microprogram on Nonlinear Partial Differential Equations |
| July 23, 2007 to August 10, 2007 |
| Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley) |
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| Return to Workshop Description |
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Stationary Ergodic Homogenization of Time Dependent Hamliton-Jacobi
Monday July 23, 2007
04:00PM - 04:50PM
Speakers:
Russell Schwab
Abstract:
The problem of stochastic homogenization of a class of convex
Hamilton-Jacobi equations of the form
$u^\ep_t+H(x/\ep,t/\ep,Du^\ep,\om)=0$ in $\real^n\times[0,T]$ is
considered. Special attention is placed on the interplay between the use
of the Subadditive Ergodic Theorem and continuity estimates for solutions
of these equations that are independent of $H_t$, $H_x$, $\om$, $\ep$ and
the final time $T$. Moreover, an inf-sup formula for the effective
Hamiltonian is provided.
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