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1996 | 33 | 1 | 127-148
Tytuł artykułu

Formation of singularities for viscosity solutions of Hamilton-Jacobi equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
33
Numer
1
Strony
127-148
Opis fizyczny
Daty
wydano
1996
Twórcy
  • Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan
  • Department of Mathematics, University of Crete, 71409 Iraklion, Crete, Greece
Bibliografia
  • [1] V. I. Arnol'd, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Birkhäuser, 1986.
  • [2] M. Bardi and L. C. Evans, On Hopf's formulas for solutions of Hamilton-Jacobi equations, Nonlinear Anal. 8 (1984), 1373-1389.
  • [3] P. Bernhard, Singular surfaces in differential games, an introduction, in: Differential Games and Applications, Lecture Notes in Control and Inform. Sci. 3, P. Hagedorn et al. (eds.), Springer, 1977, 1-33.
  • [4] A. Bogaevskiĭ, Modifications of singularities of minimum functions and bifurcations of shock waves at the Burgers equation with vanishing viscosity, Leningrad Math. J. 1 (1990), 807-823.
  • [5] M. G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67.
  • [6] M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42.
  • [7] M. G. Crandall, L. C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc 282 (1984), 487-502.
  • [8] L. C. Evans and P. E. Souganides, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J. 33 (1984), 773-797.
  • [9] W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, 1993.
  • [10] V. A. Florin, Some simplest nonlinear problems of the consolidation of an aqueously saturated earthen medium, Izv. Akad. Nauk SSSR Otdel.Tekhn. Nauk 9 (1948), 1389-1397.
  • [11] E. Hopf, Generalized solution of non-linear equations of first order, J. Math. Mech. 14 (1965), 951-973.
  • [12] R. Isaacs, Differential Games, Wiley, New York , 1965.
  • [13] S. Izumiya, Geometric singularities for Hamilton-Jacobi equation, Adv. Stud. Pure Math. 22 (1993), 89-100.
  • [14] S. Izumiya, The theory of Legendrian unfoldings and first order differential equations, Proc. Roy. Soc. Edinburgh 123A (1993), 517-532.
  • [15] S. Izumiya and G. T. Kossioris, Semi-local classification of geometric singularities for Hamilton-Jacobi equations, J. Differential Equations 118 (1995), 166-193.
  • [16] S. Izumiya and G. T. Kossioris, Realization theorem of geometric singularities for Hamilton-Jacobi equations, preprint.
  • [17] G. T. Kossioris, Propagation of singularities for viscosity solutions of Hamilton-Jacobi equations in one space variable, Comm. Partial Differential Equations 18 (1993), 747-770.
  • [18] G. T. Kossioris, Formation of singularities for viscosity solutions of Hamilton-Jacobi equations in higher dimensions, ibid., 1085-1108.
  • [19] S. Nakane, Formation of shocks for a single conservation law, SIAM J. Math. Anal. 19 (1988), 1391-1408.
  • [20] S. Nakane, Formation of singularities for Hamilton-Jacobi equations in several space variables, J. Math. Soc. Japan 43 (1991), 89-100.
  • [21] H. Rund, The Hamilton-Jacobi Theory in the Calculus of Variations, D. Van Nostrand, London, 1966.
  • [22] M. Tsuji, Solution globale et propagation des singularités pour l'équation de Hamilton-Jacobi, C. R. Acad. Sci. Paris 289 (1979), 397-400.
  • [23] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ. 26 (1986), 299-308.
  • [24] V. M. Zakalyukin, Reconstructions of fronts and caustics depending on a parameter and versality of mappings, Itogi Nauki, Contemporary Problems in Mathematics 22 (1983), 53-93.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv33z1p127bwm
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