Viscosity solutions for the dynamic programming equations |
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Authors: | Daniel Tataru |
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Institution: | (1) Department of Mathematics, University of Iasi, 6600 Iasi, Romania |
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Abstract: | In a previous paper the author has introduced a new notion of a (generalized) viscosity solution for Hamilton-Jacobi equations with an unbounded nonlinear term. It is proved here that the minimal time function (resp. the optimal value function) for time optimal control problems (resp. optimal control problems) governed by evolution equations is a (generalized) viscosity solution for the Bellman equation (resp. the dynamic programming equation). It is also proved that the Neumann problem in convex domains may be viewed as a Hamilton-Jacobi equation with a suitable unbounded nonlinear term. |
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Keywords: | Hamilton-Jacobi equation Viscosity solution Optimal control Neumann problem |
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