Parabolic differential-functional inequalities in viscosity sense

• Autorzy: Krzysztof Topolski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

viscosity solution   differential-functional equation  

Kategorie tematyczne

• 35B30: Dependence of solutions on initial and boundary data, parameters
• 35D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 1
• Strony: 17-25

Daty

wydano

1998

otrzymano

1995-04-10

Twórcy

autor

Krzysztof Topolski

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

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