Formation of singularities for viscosity solutions of Hamilton-Jacobi equations

Shyuichi Izumiya; Georgios Kossioris

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 127-148
  • ISSN: 0137-6934

How to cite

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Izumiya, Shyuichi, and Kossioris, Georgios. "Formation of singularities for viscosity solutions of Hamilton-Jacobi equations." Banach Center Publications 33.1 (1996): 127-148. <http://eudml.org/doc/262847>.

@article{Izumiya1996,
author = {Izumiya, Shyuichi, Kossioris, Georgios},
journal = {Banach Center Publications},
keywords = {evolution of singularities; contact discontinuity},
language = {eng},
number = {1},
pages = {127-148},
title = {Formation of singularities for viscosity solutions of Hamilton-Jacobi equations},
url = {http://eudml.org/doc/262847},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Izumiya, Shyuichi
AU - Kossioris, Georgios
TI - Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 127
EP - 148
LA - eng
KW - evolution of singularities; contact discontinuity
UR - http://eudml.org/doc/262847
ER -

References

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  3. [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. [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. Zbl0732.35083
  5. [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. Zbl0755.35015
  6. [6] M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. 
  7. [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. Zbl0543.35011
  8. [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. Zbl1169.91317
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  11. [11] E. Hopf, Generalized solution of non-linear equations of first order, J. Math. Mech. 14 (1965), 951-973. Zbl0168.35101
  12. [12] R. Isaacs, Differential Games, Wiley, New York , 1965. 
  13. [13] S. Izumiya, Geometric singularities for Hamilton-Jacobi equation, Adv. Stud. Pure Math. 22 (1993), 89-100. Zbl0837.35090
  14. [14] S. Izumiya, The theory of Legendrian unfoldings and first order differential equations, Proc. Roy. Soc. Edinburgh 123A (1993), 517-532. Zbl0786.35033
  15. [15] S. Izumiya and G. T. Kossioris, Semi-local classification of geometric singularities for Hamilton-Jacobi equations, J. Differential Equations 118 (1995), 166-193. Zbl0837.35091
  16. [16] S. Izumiya and G. T. Kossioris, Realization theorem of geometric singularities for Hamilton-Jacobi equations, preprint. Zbl0921.35004
  17. [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. Zbl0803.35087
  18. [18] G. T. Kossioris, Formation of singularities for viscosity solutions of Hamilton-Jacobi equations in higher dimensions, ibid., 1085-1108. Zbl0790.35068
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