Computational Mathematics and Modeling

, Volume 11, Issue 4, pp 391–400 | Cite as

Generalized Hopf formulas for the nonautonomous Hamilton-Jacobi equation

  • I. V. Rublev
Mathematical Modeling


Generalized Hopf formulas are provided for minimax (viscosity) solutions of Hamilton-Jacobi equations of the formVt+H(t, DxV)=0 andVt+H(t, V, DxV)=0 with the boundary conditionV (T, x)=ϕ(x), where ϕ is a convex function. The bounds within which these formulas apply are elucidated.


Mathematical Modeling Computational Mathematic Industrial Mathematic Convex Function Hopf Formula 
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© Kluwer Academic/Plenum Publishers 2000

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  • I. V. Rublev

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