On the uniqueness of viscosity solutions for first order partial differential-functional equations

Krzysztof Topolski

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 1, page 65-75
  • ISSN: 0066-2216

Abstract

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We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.

How to cite

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Krzysztof Topolski. "On the uniqueness of viscosity solutions for first order partial differential-functional equations." Annales Polonici Mathematici 59.1 (1994): 65-75. <http://eudml.org/doc/262339>.

@article{KrzysztofTopolski1994,
abstract = {We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.},
author = {Krzysztof Topolski},
journal = {Annales Polonici Mathematici},
keywords = {uniqueness; viscosity solution; differential-functional equation; almost everywhere solution; viscosity solutions},
language = {eng},
number = {1},
pages = {65-75},
title = {On the uniqueness of viscosity solutions for first order partial differential-functional equations},
url = {http://eudml.org/doc/262339},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Krzysztof Topolski
TI - On the uniqueness of viscosity solutions for first order partial differential-functional equations
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 1
SP - 65
EP - 75
AB - We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
LA - eng
KW - uniqueness; viscosity solution; differential-functional equation; almost everywhere solution; viscosity solutions
UR - http://eudml.org/doc/262339
ER -

References

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  1. [1] A. Augustynowicz and Z. Kamont, On Kamke's functions in uniqueness theorems for first order partial differential-functional equations, Nonlinear Anal. 14 (1990), 837-850. Zbl0738.35014
  2. [2] 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
  3. [3] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. 
  4. [4] Z. Kamont, On the Cauchy problem for system of first order partial differential-functional equations, Serdica 5 (1979), 327-339. Zbl0446.35029
  5. [5] S. N. Kruzhkov, Generalized solutions of nonlinear first order partial differential equations, Mat. Sb. 70 (1966), 394-415 (in Russian). 
  6. [6] S. N. Kruzhkov, Generalized solutions of the Hamilton-Jacobi equations of eikonal type. I, Mat. Sb. 98 (1975), 450-493 (in Russian). 
  7. [7] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Academic Press, New York, 1969. Zbl0177.12403
  8. [8] H. Leszczyński, A contribution to the uniqueness theory for first-order partial differential-functional systems, Dissertationes Math., to appear. Zbl0797.35160
  9. [9] P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982. 
  10. [10] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967. 

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