Book Review

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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.

**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