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Existence of viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0506.35020

MSC:
35F20 Nonlinear first-order PDEs
35F25 Initial value problems for nonlinear first-order PDEs
35L60 First-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
70H20 Hamilton-Jacobi equations in mechanics
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References:
[1] {\scG. Barles}, Ann. I.H.P. Anal. Nonlin., in press.
[2] Crandall, M.G; Evans, L.C; Lions, P.-L, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. amer. math. soc., 282, 487-502, (1984) · Zbl 0543.35011
[3] Crandall, M.G; Lions, P.-L, Viscosity solutions of Hamilton-Jacobi equations, Trans. amer. math. soc., 277, 1-42, (1983) · Zbl 0599.35024
[4] {\scM. G. Crandall and P.-L. Lions}, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp., in press. · Zbl 0556.65076
[5] Fleming, W.H, The Cauchy problem for degenerate parabolic equations, J. math. mech., 13, 987-1008, (1964) · Zbl 0192.19602
[6] Fleming, W.H, Nonlinear partial differential equations: probabilistic and game theoretic methods, () · Zbl 0225.35020
[7] Friedman, A, The Cauchy problem for first order partial differential equations, Indiana univ. math. J., 23, 27-40, (1973) · Zbl 0243.35014
[8] Lions, P.-L, Generalized solutions of Hamilton-Jacobi equations, Pitman lecture notes, (1982), London
[9] Lions, P.-L, Existence results for first-order Hamilton-Jacobi equations, Ricerche math., 32, 3-23, (1983) · Zbl 0552.70012
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