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.
@article{bwmeta1.element.bwnjournal-article-apmv68z1p17bwm, author = {Krzysztof Topolski}, title = {Parabolic differential-functional inequalities in viscosity sense}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {17-25}, zbl = {0898.35108}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z1p17bwm} }
Krzysztof Topolski. Parabolic differential-functional inequalities in viscosity sense. Annales Polonici Mathematici, Tome 69 (1998) pp. 17-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z1p17bwm/
[000] [1] S. Brzychczy, Chaplygin's method for a system of nonlinear parabolic differential-functional equations, Differentsial'nye Uravneniya 22 (1986), 705-708 (in Russian). | Zbl 0613.35041
[001] [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. | Zbl 0657.35126
[002] [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.
[003] [4] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42.
[004] [5] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Academic Press, New York, 1969. | Zbl 0177.12403
[005] [6] P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982.
[006] [7] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.
[007] [8] J. Szarski, Sur un système non linéaire d'inégalités différentielles paraboliques contenant des fonctionnelles, Colloq. Math. 16 (1967), 141-145. | Zbl 0148.34802
[008] [9] J. Szarski, Uniqueness of solutions of mixed problem for parabolic differential-functional equations, Ann. Polon. Math. 28 (1973), 52-65. | Zbl 0264.35039
[009] [10] K. Topolski, On the uniqueness of viscosity solutions for first order partial differential-functional equations, Ann. Polon. Math. 59 (1994), 65-75. | Zbl 0804.35138