Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

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

Retrieve article in: PDF

Book Information

Author(s): 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:

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


Additional Information:

Reviewer(s):
Stanley H. Benton

Review Information:
Journal: Bull. Amer. Math. Soc. 9 (1983), 252-256.
DOI: 10.1090/S0273-0979-1983-15174-1
PII: S 0273-0979(1983)15174-1


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google