Parabolic differential-functional inequalities in viscosity sense

Krzysztof Topolski

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 1, page 17-25
  • ISSN: 0066-2216

Abstract

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We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.

How to cite

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Krzysztof Topolski. "Parabolic differential-functional inequalities in viscosity sense." Annales Polonici Mathematici 68.1 (1998): 17-25. <http://eudml.org/doc/270342>.

@article{KrzysztofTopolski1998,
abstract = {We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.},
author = {Krzysztof Topolski},
journal = {Annales Polonici Mathematici},
keywords = {viscosity solution; differential-functional equation; viscosity solutions; mixed problems; subsolutions; supersolutions},
language = {eng},
number = {1},
pages = {17-25},
title = {Parabolic differential-functional inequalities in viscosity sense},
url = {http://eudml.org/doc/270342},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Krzysztof Topolski
TI - Parabolic differential-functional inequalities in viscosity sense
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 1
SP - 17
EP - 25
AB - We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.
LA - eng
KW - viscosity solution; differential-functional equation; viscosity solutions; mixed problems; subsolutions; supersolutions
UR - http://eudml.org/doc/270342
ER -

References

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  1. [1] S. Brzychczy, Chaplygin's method for a system of nonlinear parabolic differential-functional equations, Differentsial'nye Uravneniya 22 (1986), 705-708 (in Russian). Zbl0613.35041
  2. [2] S. Brzychczy, Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain, Ann. Polon. Math. 47 (1987), 309-317. Zbl0657.35126
  3. [3] 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. 
  4. [4] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. 
  5. [5] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Academic Press, New York, 1969. Zbl0177.12403
  6. [6] P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982. 
  7. [7] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967. 
  8. [8] J. Szarski, Sur un système non linéaire d'inégalités différentielles paraboliques contenant des fonctionnelles, Colloq. Math. 16 (1967), 141-145. Zbl0148.34802
  9. [9] J. Szarski, Uniqueness of solutions of mixed problem for parabolic differential-functional equations, Ann. Polon. Math. 28 (1973), 52-65. Zbl0264.35039
  10. [10] K. Topolski, On the uniqueness of viscosity solutions for first order partial differential-functional equations, Ann. Polon. Math. 59 (1994), 65-75. Zbl0804.35138

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