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- W2160487777 abstract "Parabolic PDEs and Deterministic Games By Robert V. Kohn Parabolic partial differential equations seem very different from first-order Hamilton–Jacobi equations. Parabolic equations are linked to random walks, and often arise as steepest descents; Hamilton–Jacobi equations have characteristics, and often arise from optimal control problems. But appearances can be deceiving. Some parabolic (and elliptic) PDEs are surprisingly similar to Hamilton–Jacobi equations. In my talk at ICIAM, I explained why, drawing on recent work with Sylvia Serfaty [7]. To keep things simple, I focus on two key examples: (i) Motion with constant velocity. Consider the evolution of a region Ω in the plane as its boundary moves inward with constant velocity 1 (Figure 1, left). The evolution is completely characterized by the arrival time u ( x ) = time at which the moving boundary passes through x. This function solves the Hamilton–Jacobi equation (1)" @default.
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- W2160487777 modified "2023-09-25" @default.
- W2160487777 title "Parabolic PDEs and Deterministic Games" @default.
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