Existence results for first order Hamilton Jacobi equations

G. Barles

Annales de l'I.H.P. Analyse non linéaire (1984)

  • Volume: 1, Issue: 5, page 325-340
  • ISSN: 0294-1449

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Barles, G.. "Existence results for first order Hamilton Jacobi equations." Annales de l'I.H.P. Analyse non linéaire 1.5 (1984): 325-340. <http://eudml.org/doc/78078>.

@article{Barles1984,
author = {Barles, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {viscosity solutions; existence results for global solutions; Dirichlet type boundary conditions; uniqueness and comparison results},
language = {eng},
number = {5},
pages = {325-340},
publisher = {Gauthier-Villars},
title = {Existence results for first order Hamilton Jacobi equations},
url = {http://eudml.org/doc/78078},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Barles, G.
TI - Existence results for first order Hamilton Jacobi equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 5
SP - 325
EP - 340
LA - eng
KW - viscosity solutions; existence results for global solutions; Dirichlet type boundary conditions; uniqueness and comparison results
UR - http://eudml.org/doc/78078
ER -

References

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  1. [1] S.H. Benton, The Hamilton Jacobi Equation. A global Approach, Academic Press, New York, 1977. Zbl0418.49001MR442431
  2. [2] E.D. Conway and E. Hopf, Hamilton's theory and generalized solutions of Hamilton Jacobi equations. J. Math. Mech., t. 12, 1964, p. 939-986. Zbl0178.11002MR182761
  3. [3] M.G. Crandall, L.C. Evans, P.L. Lions, Some properties of viscosity solutions of Hamilton Jacobi equations. To appear in Trans. Amer. Math. Soc., 1983. Zbl0543.35011MR732102
  4. [4] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton Jacobi equations. To appear in Trans. Amer. Math. Soc., 1983. Zbl0599.35024MR690039
  5. [5] A. Douglis, The continuous dependance of generalized solutions of non linear partial differential equations upon initial data. Comm. Pure Applied Math., t. 14, 1961, p. 267-284. Zbl0117.31102MR139848
  6. [6] W.H. Fleming, The Cauchy problem for a non linear partial differential. J. Diff. equations, t. 5, 1969, p. 515-530. Zbl0172.13901MR235269
  7. [7] W.H. Fleming, Nonlinear partial differential equations-probabilistie and game theoretic method. In Problems in Nonlinear Analysis, CIME Ed. Cremonese, Roma, 1971. Zbl0225.35020MR282048
  8. [8] W.H. Fleming, The Cauchy problem for degenerate parabolic equations. J. Math. Mech., t. 13, 1964, p. 987-1008. Zbl0192.19602MR179473
  9. [9] A. Friedman, The Cauchy problem for first order partial differential equations. Indiana Univ. Mat. J., t. 23, 1973, p. 27-40. Zbl0243.35014MR326136
  10. [10] S.N. Kruzkov, Generalized solutions of Hamilton Jacobi equations of Eikonal type. I. USSR Sbornik, t. 27, 1975, p. 406-446. Zbl0369.35012
  11. [11] S.N. Kruzkov, Generalized solutions of nonlinear first order equations and certain quasilinear parabolic equations Vestnik Moscow unio Ser. I. Math. Mech., t. 6, 1964, p. 67-74 (In Russian). 
  12. [12] S.N. Kruskov, Generalized solutions of first order nonlinear equations in several independant variables. I. Mat. Sb., t. 70, 112, 1966, p. 394-415, II. Mat. Sb. (N. S.), t. 72, 114, 1967, p. 93-116 (in Russian). Zbl0164.40802
  13. [13] P.L. Lions, Generalized solutions of Hamilton Jacobi equations. PitmanLondon, 1982, Zbl0497.35001MR667669
  14. [14] P.L. Lions, Existence results for first order Hamilton Jacobi equations. To appear in Ric. Mat. Zbl0552.70012MR740198
  15. [15] P.E. Souganidis, Existence of viscosity solutions of Hamilton Jacobi equations. Zbl0506.35020

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