Acta mathematica scientia, Series B >
THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS
Received date: 2011-09-20
Online published: 2011-11-20
Supported by
This research was supported by National Natural Science Foundation of China (10871133, 11071246 and 11101143), Fundamental Research Funds of the Central Universities (09QL48). †Corresponding author: Wen Hairui.
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 hypersurface tends asymptotically to a given hypersurface with rate t−1/4 .
Wang Jinghua , Wen Hairui , Zhao Yinchuan . THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(6) : 2265 -2277 . DOI: 10.1016/S0252-9602(11)60398-6
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