THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS |
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| Authors: | Wang Jinghua Academy of Mathematics System Sciences The Chinese Academy of Sciences Beijing China Wen Hairui |
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| Affiliation: | Wang Jinghua Academy of Mathematics and System Sciences,The Chinese Academy of Sciences,Beijing 100190,China Wen Hairui Department of Mathematics,Beijing Institute of Technology,Beijing 100081,China Zhao Yinchuan Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China |
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| Abstract: | We use Hopf-Lax formula to study local regularity of solution to Hamilton-Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T > 0, which depends only on the Hamiltonian and initial datum, for t > T the solution of the IVP (1.1) is smooth except for a smooth n-dimensional hypersurface, across which Du(x, t) is discontinuous. And we show that the hypersu... |
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| Keywords: | Hopf-Lax formula Hamilton-Jacobi equations local regularity large time generic form |
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