Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: P. L. Lions
Title: Generalized solutions of Hamilton-Jacobi equations
Additional book information: Research Notes in Mathematics, Vol. 69, Pitman Advanced Publishing Program, Boston, 1982, 317 pp., $24.95. ISBN 0-2730-8556-5.

References [Enhancements On Off] (What's this?)

  • 1. S. Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in one space variable, Hiroshima Math. J. 3 (1973), 367-386. MR 346300
  • 2. S. Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in several space variables, Hiroshima Math. J. 6 (1976), 15-30. MR 393779
  • 3. S. Aizawa and N. Kikuchi, A mixed initial and boundary-value problem for the Hamilton-Jacobi equation in several space variables, Funkcial. Ekvac. 9 (1966), 139-150. MR 211056
  • 4. S. H. Benton, A general space-time boundary value problem for the Hamilton-Jacobi equation, J. Differential Equations 11 (1972), 425-435. MR 298196
  • 5. S. H. Benton, Global variational solutions of Hamilton-Jacobi boundary value problems, J. Differential Equations 13 (1973), 468-480. MR 402253
  • 6. S. H. Benton, The Hamilton-Jacobi equation: a global approach, Academic Press, New York, 1977. MR 442431
  • 7. B. C. Burch, A semigroup approach to the Hamilton-Jacobi equation, Tulane Univ. dissertation, New Orleans, 1975.
  • 8. B. C. Burch, A semigroup treatment of the Hamilton-Jacobi equation in several space variables, J. Differential Equations 23 (1977), 107-124. MR 440183
  • 9. J. D. Cole, On a quasilinear parabolic equation occurring in aerodynamics. Quart. Appl. Math. 9 (1951), 225-236. MR 42889
  • 10. E. D. Conway and E. Hopf, Hamilton's theory and generalized solutions of the Hamilton-Jacobi equation, J. Math. Mech. 13 (1964), 939-986. MR 182761
  • 11. M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265-298. MR 287357
  • 12. A. Douglis, Solutions in the large for multi-dimensional non-linear partial differential equations of first order, Ann. Inst. Fourier (Grenoble) 15 (1965), 1-35. MR 199542
  • 13. A. Douglis, Layering methods for nonlinear partial differential equations of first order, Ann. Inst. Fourier (Grenoble) 22 (1972), 141-227. MR 358089
  • 14. R. J. Elliott and N. J. Kalton, The existence of value in differential games, Amer. Math. Soc. Mem. No. 126 (1972). MR 359845
  • 15. R. J. Elliott and N. J. Kalton, The existence of value in differential games of pursuit and evasion, J. Differential Equations 12 (1972), 504-523. MR 359846
  • 16. R. J. Elliott and N. J. Kalton, Cauchy problems for certain Isaacs-Bellman equations and games of survival, Trans. Amer. Math. Soc. 198 (1974), 45-72. MR 347383
  • 17. R. J. Elliott and N. J. Kalton, Boundary value problems for nonlinear partial differential operators, J. Math. Anal. Appl. 46 (1974), 228-241. MR 395887
  • 18. E. E. Feltus, Mixed problems for the Hamilton-Jacobi equation, Tulane Univ. dissertation, New Orleans, 1975.
  • 19. W. H. Fleming, The Cauchy Problem for a nonlinear first order partial differential equation, J. Differential Equations 5 (1969), 515-530. MR 235269
  • 20. A. R. Forsyth, Theory of differential equations, Vols. 5 and 6, Dover, New York, 1959. MR 123757
  • 21. E. Hopf, The partial differential equation u + uu = µu, Comm. Pure Appl. Math. 3 (1950), 201-230.
  • 22. E. Hopf, Generalized solutions of non-linear equations of first order, J. Math. Mech. 14 (1965), 951-974. MR 182790
  • 23. S. N. Kruzkov, Generalized solutions of nonlinear first order equations with several independent variables. II, Mat. Sb. 72; English transl. in Math. USSR Sb. 1 (1967), 93-116. MR 204847
  • 24. P. D. Lax, Nonlinear hyperbolic equations, Comm. Pure Appl. Math. 6 (1953), 231-258. MR 56176
  • 25. P. D. Lax, The initial value problem for nonlinear hyperbolic equations in two independent variables, Ann. Math. Studies 33 (1954), 211-229. MR 68093
  • 26. P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 (1954), 159-193. MR 66040
  • 27. P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 93653
  • 28. O. A. Oleinik, Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk. 12; English transl. in Amer. Math. Soc. Transl. (2) 26 (1957), 95-172. MR 151737

Review Information:

Reviewer: Stanley H. Benton
Journal: Bull. Amer. Math. Soc. 9 (1983), 252-256
DOI: https://doi.org/10.1090/S0273-0979-1983-15174-1
American Mathematical Society