Hopf formula and multitime Hamilton-Jacobi equations
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- by P.-L. Lions and J.-C. Rochet PDF
- Proc. Amer. Math. Soc. 96 (1986), 79-84 Request permission
Abstract:
Problems arising in mathematical economics lead to the study of multi-time Hamilton-Jacobi equations. Using commutation properties of the semigroups for the standard equation, we propose a generalization of the Hopf formula that gives explicit solutions of these equations.References
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M. Bardi and L. C Evans, On Hopf’s formulas for solutions of Hamilton-Jacobi equations, preprint.
- Michael G. Crandall and Pierre-Louis Lions, Condition d’unicité pour les solutions généralisées des équations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 3, 183–186 (French, with English summary). MR 610314
- Michael G. Crandall and Pierre-Louis Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), no. 1, 1–42. MR 690039, DOI 10.1090/S0002-9947-1983-0690039-8 —, Solutions de viscosité non bornées des équations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris (in preparation).
- Eberhard Hopf, Generalized solutions of non-linear equations of first order, J. Math. Mech. 14 (1965), 951–973. MR 0182790
- Hitoshi Ishii, Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984), no. 5, 721–748. MR 756156, DOI 10.1512/iumj.1984.33.33038
- P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI 10.1002/cpa.3160100406
- Pierre-Louis Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, vol. 69, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 667669
- P.-L. Lions and Makiko Nisio, A uniqueness result for the semigroup associated with the Hamilton-Jacobi-Bellman operator, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 7, 273–276. MR 682680 J. C. Rochet, The taxation principle and multi-time Hamilton-Jacobi equations, preprint, Univ. Paris IX.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 79-84
- MSC: Primary 35F99; Secondary 35L40, 90A16
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813815-5
- MathSciNet review: 813815