Book Review

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MathSciNet review: 1567454

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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.

*A semigroup treatment of the Hamilton-Jacobi equation in one space variable*, Hiroshima Math. J.

**3**(1973), 367–386. MR

**346300**

*A semigroup treatment of the Hamilton-Jacobi equation in several space variables*, Hiroshima Math. J.

**6**(1976), no. 1, 15–30. MR

**393779**

*A mixed initial and boundary-value problem for the Hamilton-Jacobi equation in several space variables*, Funkcial. Ekvac.

**9**(1966), 139–150. MR

**211056**

*A general space-time boundary value problem for the Hamilton-Jacobi equation*, J. Differential Equations

**11**(1972), 425–435. MR

**298196**, DOI 10.1016/0022-0396(72)90056-3

*Global variational solutions of Hamilton-Jacobi boundary value problems*, J. Differential Equations

**13**(1973), 468–480. MR

**402253**, DOI 10.1016/0022-0396(73)90005-3

*The Hamilton-Jacobi equation*, Mathematics in Science and Engineering, Vol. 131, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. A global approach. MR

**0442431**

**7.**

*A semigroup approach to the Hamilton-Jacobi equation*, Tulane Univ. dissertation, New Orleans, 1975.

*A semigroup treatment of the Hamilton-Jacobi equation in several space variables*, J. Differential Equations

**23**(1977), no. 1, 107–124. MR

**440183**, DOI 10.1016/0022-0396(77)90137-1

*On a quasi-linear parabolic equation occurring in aerodynamics*, Quart. Appl. Math.

**9**(1951), 225–236. MR

**42889**, DOI 10.1090/S0033-569X-1951-42889-X

*Hamilton’s theory and generalized solutions of the Hamilton-Jacobi equation*, J. Math. Mech.

**13**(1964), 939–986. MR

**0182761**

*Generation of semi-groups of nonlinear transformations on general Banach spaces*, Amer. J. Math.

**93**(1971), 265–298. MR

**287357**, DOI 10.2307/2373376

*Solutions in the large for multi-dimensional, non-linear partial differential equations of first order*, Ann. Inst. Fourier (Grenoble)

**15**(1965), no. fasc. 2, 1–35. MR

**199542**

*Layering methods for nonlinear partial differential equations of first order*, Ann. Inst. Fourier (Grenoble)

**22**(1972), no. 3, 141–227 (English, with French summary). MR

**358089**

*The existence of value in differential games*, Memoirs of the American Mathematical Society, No. 126, American Mathematical Society, Providence, R.I., 1972. MR

**0359845**

*The existence of value in differential games of pursuit and evasion*, J. Differential Equations

**12**(1972), 504–523. MR

**359846**, DOI 10.1016/0022-0396(72)90022-8

*Cauchy problems for certain Isaacs-Bellman equations and games of survival*, Trans. Amer. Math. Soc.

**198**(1974), 45–72. MR

**347383**, DOI 10.1090/S0002-9947-1974-0347383-8

*Boundary value problems for nonlinear partial differential operators*, J. Math. Anal. Appl.

**46**(1974), 228–241. MR

**395887**, DOI 10.1016/0022-247X(74)90293-5

**18.**

*Mixed problems for the Hamilton-Jacobi equation*, Tulane Univ. dissertation, New Orleans, 1975.

*The Cauchy problem for a nonlinear first order partial differential equation*, J. Differential Equations

**5**(1969), 515–530. MR

**235269**, DOI 10.1016/0022-0396(69)90091-6

*Theory of differential equations. 1. Exact equations and Pfaff’s problem; 2, 3. Ordinary equations, not linear; 4. Ordinary linear equations; 5, 6. Partial differential equations*, Dover Publications, Inc., New York, 1959. Six volumes bound as three. MR

**0123757**

**21.**

*The partial differential equation u*+

*uu*=

*µu*, Comm. Pure Appl. Math. 3 (1950), 201-230.

*Generalized solutions of non-linear equations of first order*, J. Math. Mech.

**14**(1965), 951–973. MR

**0182790**

*Generalized solutions of nonlinear equations of the first order with several independent variables. II*, Mat. Sb. (N.S.)

**72 (114)**(1967), 108–134 (Russian). MR

**0204847**

*Nonlinear hyperbolic equations*, Comm. Pure Appl. Math.

**6**(1953), 231–258. MR

**56176**, DOI 10.1002/cpa.3160060204

*The initial value problem for nonlinear hyperbolic equations in two independent variables*, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 211–229. MR

**0068093**

*Weak solutions of nonlinear hyperbolic equations and their numerical computation*, Comm. Pure Appl. Math.

**7**(1954), 159–193. MR

**66040**, DOI 10.1002/cpa.3160070112

*Hyperbolic systems of conservation laws. II*, Comm. Pure Appl. Math.

**10**(1957), 537–566. MR

**93653**, DOI 10.1002/cpa.3160100406

*Discontinuous solutions of non-linear differential equations*, Amer. Math. Soc. Transl. (2)

**26**(1963), 95–172. MR

**0151737**, DOI 10.1090/trans2/026/05

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