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.
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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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