Souganidis, Panagiotis E. Max-min representations and product formulas for the viscosity solutions of Hamilton-Jacobi equations with applications to differential games. (English) Zbl 0526.35018 Nonlinear Anal., Theory Methods Appl. 9, 219-257 (1985). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 22 Documents MSC: 35F20 Nonlinear first-order PDEs 35C99 Representations of solutions to partial differential equations 35D99 Generalized solutions to partial differential equations 49K35 Optimality conditions for minimax problems 47H99 Nonlinear operators and their properties 35F25 Initial value problems for nonlinear first-order PDEs 91A23 Differential games (aspects of game theory) 91A99 Game theory 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 49J35 Existence of solutions for minimax problems 35L60 First-order nonlinear hyperbolic equations Keywords:max-min representations; product formulas; viscosity solutions; Hamilton- Jacobi equations; generalized solutions; Trotter products; explicit error estimates; approximation schemes Citations:Zbl 0469.49023 PDFBibTeX XMLCite \textit{P. E. Souganidis}, Nonlinear Anal., Theory Methods Appl. 9, 219--257 (1985; Zbl 0526.35018) Full Text: DOI References: [1] Barles, G., Thèse de Doctorat 3ème Cycle, (Trans. Am. math. Soc. (1982-1983), Université de Paris IX-Dauphine), (to appear). [2] Barron N. E., Evans L. C. & Jensen R., Viscosity solutions of Isaacs’ equations and differential games with Lipschitz controls, J. diff. Eqns; Barron N. E., Evans L. C. & Jensen R., Viscosity solutions of Isaacs’ equations and differential games with Lipschitz controls, J. diff. Eqns · Zbl 0548.90104 [3] Crandall, M. G.; Evans, L. C.; Lions, P. L., Some properties of viscosity solutions of Hamilton-Jacobi equations, (Mathematics Research Center TSR No. 2390 (June 1982), University of Wisconsin-Madison). (Mathematics Research Center TSR No. 2390 (June 1982), University of Wisconsin-Madison), Trans. Am. math. Soc., 282, 487-502 (1984) · Zbl 0543.35011 [4] Crandall, M. G.; Lions, P. L., Viscosity solutions of Hamilton-Jacobi equations, Trans. 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L. & Souganidis P., Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations, SIAM J. Control Optim.; Lions P. L. & Souganidis P., Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations, SIAM J. Control Optim. · Zbl 0569.49019 [22] Souganidis, P. E., Existence of viscosity solutions of Hamilton-Jacobi equations, (Mathematics Research Center TSR No. 2488. Mathematics Research Center TSR No. 2488, J. diff. Eqns (March 1983), University of Wisconsin-Madison), (to appear) · Zbl 0598.35066 [23] Souganidis, P. E., Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, (Mathematics Research Center TSR No. 2511 (April 1983), University of Wisconsin-Madison) · Zbl 0598.35066 [24] Souganidis P. E., Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. diff. Eqns.; Souganidis P. E., Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. diff. Eqns. · Zbl 0536.70020 [25] Subbotin, A., A generalization of the basic equation of the theory of differential games, Soviet Math. Dokl., 22, 358-362 (1980) · Zbl 0467.90095 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.