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Souganidis, Panagiotis E.

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

J. Differ. Equations 56, 345-390 (1985).
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Cited in 1 Review
Cited in 42 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
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\textit{P. E. Souganidis}, J. Differ. Equations 56, 345--390 (1985; Zbl 0506.35020)
Full Text: DOI

References:

[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
[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, (Problems in Nonlinear Analysis (1971), Cremonese, Ed. Collect. IME: Cremonese, Ed. Collect. IME Rome) · 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 · Zbl 0497.35001
[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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