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1994 | 59 | 1 | 65-75
Tytuł artykułu

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

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EN
Abstrakty
EN
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.
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [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.
  • [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.
  • [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.
  • [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.
  • [8] H. Leszczyński, A contribution to the uniqueness theory for first-order partial differential-functional systems, Dissertationes Math., to appear.
  • [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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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv59z1p65bwm
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