Bulletin of the American Mathematical Society

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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.

Sadakazu Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in one space variable, Hiroshima Math. J. 3 (1973), 367–386. MR 346300

Sadakazu Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in several space variables, Hiroshima Math. J. 6 (1976), no. 1, 15–30. MR 393779

Sadakazu Aizawa and Norio 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

Stanley H. Benton Jr., 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

Stanley H. Benton Jr., 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

Stanley H. Benton Jr., 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.

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

B. C. Burch, 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

Julian D. Cole, 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

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 0182761

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, DOI 10.2307/2373376

Avron Douglis, 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

Avron Douglis, 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

Robert J. Elliott and Nigel J. Kalton, The existence of value in differential games, Memoirs of the American Mathematical Society, No. 126, American Mathematical Society, Providence, R.I., 1972. MR 0359845

Robert J. Elliott and Nigel J. Kalton, 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

Robert J. Elliott and Nigel J. Kalton, 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

Robert J. Elliott and Nigel J. Kalton, 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.

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

Wendell H. Fleming, 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

Andrew Russell Forsyth, 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.

E. Hopf, The partial differential equation u + uu = µu, Comm. Pure Appl. Math. 3 (1950), 201-230.

Eberhard Hopf, Generalized solutions of non-linear equations of first order, J. Math. Mech. 14 (1965), 951–973. MR 0182790

S. N. Kružkov, 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

Peter D. Lax, Nonlinear hyperbolic equations, Comm. Pure Appl. Math. 6 (1953), 231–258. MR 56176, DOI 10.1002/cpa.3160060204

P. D. Lax, 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

Peter D. Lax, 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

P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI 10.1002/cpa.3160100406

O. A. Oleĭnik, Discontinuous solutions of non-linear differential equations, Amer. Math. Soc. Transl. (2) 26 (1963), 95–172. MR 0151737, DOI 10.1090/trans2/026/05

1.

S. Aizawa, A semigroup treatment of the Hamilton-Jacobi equation in one space variable, Hiroshima Math. J. 3 (1973), 367-386. MR 0346300

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