Generalized solutions by Cauchy's method of characteristics

Ştefan Mirică

Rendiconti del Seminario Matematico della Università di Padova (1987)

  • Volume: 77, page 317-350
  • ISSN: 0041-8994

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Mirică, Ştefan. "Generalized solutions by Cauchy's method of characteristics." Rendiconti del Seminario Matematico della Università di Padova 77 (1987): 317-350. <http://eudml.org/doc/108068>.

@article{Mirică1987,
author = {Mirică, Ştefan},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {method of characteristics; generalized solutions; first-order Hamilton- Jacobi equations},
language = {eng},
pages = {317-350},
publisher = {Seminario Matematico of the University of Padua},
title = {Generalized solutions by Cauchy's method of characteristics},
url = {http://eudml.org/doc/108068},
volume = {77},
year = {1987},
}

TY - JOUR
AU - Mirică, Ştefan
TI - Generalized solutions by Cauchy's method of characteristics
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1987
PB - Seminario Matematico of the University of Padua
VL - 77
SP - 317
EP - 350
LA - eng
KW - method of characteristics; generalized solutions; first-order Hamilton- Jacobi equations
UR - http://eudml.org/doc/108068
ER -

References

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  1. [1] R. Abraham - J. ROBBIN, Transversal Mappings and Flows, Benjamin, New York, 1967. Zbl0171.44404MR240836
  2. [2] S.H. Benton jr., The Hamilton-Jacobi equation. A global approach, Academic Press, New York, 1977. Zbl0418.49001MR442431
  3. [3] V.G. Boltyanskii, Mathematical Methods of Optimal Control, Holt, Rinehart & Winston, New York, 1971. Zbl0213.15504MR353081
  4. [4] P. Brunovsky, Existence of regular synthesis for general control problems, J. Differential Equations, 38 (1980), pp. 317-343. Zbl0417.49030MR605053
  5. [5] L. Cesari, Optimization. Theory and Applications, Springer, New York, 1983. Zbl0506.49001MR688142
  6. [6] F.H. Clarke, Optimal control and the true hamiltonian, SIAM Review, 21 (1979), pp. 157-166. Zbl0408.49025MR524510
  7. [7] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. II, Wiley, New York, 1962. Zbl0099.29504MR1013360
  8. [8] M.G. Crandal - L.C. Evans - P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. A.M.S., 282, 2 (1984), pp. 487-502. Zbl0543.35011MR732102
  9. [9] R.P. Fedorenko, On the Cauchy problem for Bellman equation of dynamic programming, Z. Vyc. Mat. i Mat. Phys., 9 (1969), pp. 426-432 (Russian). Zbl0224.49020MR258448
  10. [10] W.H. Fleming, The Cauchy problem for a nonlinear first order partial differential equation, J. Differential Equations, 5 (1969), pp . 515-530. Zbl0172.13901MR235269
  11. [11] A. Halanay, Differential Equations, Ed. Did. Pedagogică, Bucuresti, 1972 (Romanian). MR355142
  12. [12] PH. Hartman, Ordinary Differential Equations, Wiley, New York, 1964. Zbl0125.32102MR171038
  13. [13] R. Isaacs, Differential Games, Wiley, New York, 1965. Zbl0125.38001MR210469
  14. [14] S. Lang, Introduction to Differentiable Manifolds, Interscience, New York, 1962. Zbl0103.15101MR155257
  15. [15] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
  16. [16] J. Mather, Stratifications and Mappings, Preprint, Harvard University (Russian transl.: Uspehi Mat. Nauk, 27 (1972), pp. 85-118). Zbl0253.58005MR385917
  17. [17] Ş. Miric, The contingent and the paratingent as generalized derivatives for vector-valued and set-valued mappings, Nonlinear Analysis. Theory, Theory & Appl., 6 (1982), pp. 1335-1368. Zbl0529.26010MR684969
  18. [18] Ş. Miric, Stratified Hamiltonians and the optimal feedback control, Ann. Mat. Pura Appl., 33 (1983), pp. 51-78. Zbl0523.49020MR725019
  19. [19] Ş. Miric, Stratified Hamilton-Jacobi equations and applications, Anal. Univ. Bucureşti, Seria Mat., 33 (1984), pp. 59-68. Zbl0546.49009MR773733
  20. [20] Ş Mirică, Dynamic programming method for stratified optimal control problems, Preprint Series in Mathematics, No. 12/1984, Increst-Inst. Inst. Mat., Bucureşti, 1984. 
  21. [21] H. Stalford, Sufficiency theorem for discontinuous optimal cost surfaces, SIAM J. Control Opt., 16 (1978), pp. 63-82. Zbl0385.49007MR487730
  22. [22] H. Sussman, Analytic stratifications and control theory, « Proc. Int. Congress of Math. » (Helsinki, 1978), pp. 865-871. Zbl0499.93023MR562701
  23. [23] M. Tamm, Subanalytic sets in the Calculus of Variations, Acta Math., 146 (1981), pp. 167-199. Zbl0478.58010MR611382
  24. [24] R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc., 75 (1969), pp. 24-284. Zbl0197.20502MR239613
  25. [25] E. Whitney, Tangents to an analytic variety, Ann. of Math., 81 (1965), pp. 496-549. Zbl0152.27701MR192520

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