Viscosity solutions of hamilton-jacobi equations

Transactions of the American Mathematical Society

Volumn 277, Issue 1, 1983, Pages 1-42

  Crandall, Michael G ^a   Lions, Pierre Louis ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Hamilton Jacobi equations; Uniqueness criteria

Indexed keywords

EID: 84967758647     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1983-0690039-8     Document Type: Article

References (27)

1. S. Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in several space variables, Hiroshima Math. J. 6 (1976), 15-30.
2. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976.
3. Anatole Beck, Uniqueness of flow solutions of differential equations, Recent Advances in Topological Dynamics, Lecture Notes in Math., vol. 318, Springer-Verlag, Berlin and New York, 1973, pp. 30-50.
4. S. H. Benton, The Hamilton-Jacobi equation: A global approach, Academic Press, New York, 1977.
5. J. M. Bony, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), 333-336.
6. E. D. Conway and E. Hopf, Hamilton's theory and generalized solutions of the Hamilton-Jacohi equation, J. Math. Mech. 13 (1964), 939-986.
7. M. G. Crandall, An introduction to evolution governed by accretive operators, Dynamical Systems—An International Symposium (L. Cesari, J. Hale, J. LaSalle, eds.), Academic Press, New York, 1976, pp. 131-165.
8. M. G. Crandall and P. L. Lions, Condition d' unicité pour les solutions généralisées des equations de Hamilton-Jacobi du \er ordre, C. R. Acad. Sci. Paris Sér. A-B 292 (1981), 183-186.
9. M. G. Crandall, Two approximations of solutions of Hamilton-Jacobi equations (to appear).
10. A. Douglis, The continuous dependence of generalized solutions of nonlinear partial differential equations upon initial data, Comm. Pure Appl. Math. 14 (1961), 267-284.
11. L. C. Evans, On solving certain nonlinear partial differential equations by accretive operator methods, Israel J. Math. 86 (1980), 225-247.
12. L. C. Evans, Application of nonlinear semigroup theory to certain partial differential equations, Nonlinear Evolution Equations (M. G. Crandall, ed.), Academic Press, New York, 1978.
13. W. H. Fleming, The Cauchy problem for a nonlinear first order partial differential equation, J. Differential Equations 5 (1969), 515-530.
14. W. H. Fleming, Nonlinear partial differential equations—probabilistic and game theoretic methods, Problems in Nonlinear Analysis, CIME, Ed. Cremonese, Roma, 1971.
15. W. H. Fleming, The Cauchy problem for degenerate parabolic equations, J. Math. Mech. 13 (1964), 987-1008.
16. A. Friedman, The Cauchy problem for first order partial differential equations, Indiana Univ. Math. J. 23(1973), 27-40.
17. E. Hopf, On the right weak solution of the Cauchy problem for a quasilinear equation of first order, J. Math. Mech. 19 (1969/70), 483-487.
18. S. N. Kruzkov, Generalized solution of the Hamilton-Jacobi equations of Eikonal type. I, Math. USSR-Sb. 27 (1975), 406-446.
19. S. N. Kruzkov, Generalized solutions of nonlinear first order equations and certain quasilinear parabolic equations, Vestnik Moscov. Univ. Ser. I Mat. Meh. 6 (1964), 61-1A. (Russian)
20. S. N. Kruzkov, Generalized solutions of first order nonlinear equations in several independent variables. I, Mat. Sb. 70 (112) (1966), 394-415; II, Mat. Sb. (N. S.) 72 (114) (1967), 93-116. (Russian)
21. S. N. Kruzkov, First order quasilinear equations with several space variables, Math. USSR-Sb. 10 (1970), 217-243.
22. P. L. Lions, Generalized solutions of Hamilton-J acobi equations, Pitman Research Notes Series, Pitman, London, 1982.
23. P. L. Lions, Control of diffusion processes in RN, Comm. Pure Appl. Math. 34 (1981), 121-147.
24. O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. 26 (1963), 95-172.
25. M. B. Tamburro, The evolution operator approach to the Hamilton-J acobi equations, Israel J. Math. 26(1977), 232-264.
26. A. I. Vol'pert, The spaces BV and quasilinear equations, Math. USSR-Sb. 2 (1967), 225-267.
27. M. G. Crandall, P. L. Lions and L. C. Evans, Some properties of viscosity solutions of Hamilton-J acobi equations, Trans. Amer. Math. Soc. (to appear).