Souganidis, Panagiotis E. Existence of viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0506.35020 J. Differ. Equations 56, 345-390 (1985). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 40 Documents 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 Keywords:existence; viscosity solutions; uniqueness PDF BibTeX XML Cite \textit{P. E. Souganidis}, J. Differ. Equations 56, 345--390 (1985; Zbl 0506.35020) Full Text: DOI OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.