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

Annales Polonici Mathematici (1994)

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

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topKrzysztof 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

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

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