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2000 | 52 | 1 | 163-173
Tytuł artykułu

Time-periodic solutions of quasilinear parabolic differential equations II. Oblique derivative boundary conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.
Słowa kluczowe
Rocznik
Tom
52
Numer
1
Strony
163-173
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
Bibliografia
  • [1] H. Amann, Periodic solutions of semi-linear parabolic equations, in: Non-linear Analysis: A Collection of Papers in Honor of Erich H. Rothe (L. Cesari, R. Kannan, H. Weinberger, eds.), Academic Press, New York 1978, 1-29.
  • [5] G. C. Dong, Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations, J. Partial Differential Equations 1 (1988), 12-42.
  • [6] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Second Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1983.
  • [7] P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Longman Scientific & Technical, Harlow, Essex, 1991.
  • [Kli] V. S. Klimov, Periodic and stationary solutions of quasilinear parabolic equations, Sib. Mat. Zh. 17 (1976), 530-532 [Russian]; English transl. in Sib. Math. J. 17 (1976), 530-533.
  • [9] S. N. Kruzhkov, Periodic solutions to nonlinear equations, Differentsial'nye Uravneniya 6 (1970), 731-740 [Russian]; English transl. in Differential Equations 6 (1970), 560-566.
  • [10] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R. I. 1968.
  • [13] G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations, Nonlinear Anal. 8 (1984) 49-65.
  • [14] G. M. Lieberman, Solvability of quasilinear elliptic equations with nonlinear boundary conditions. II, J. Functional Anal. 56 (1984), 210-219.
  • [17] G. M. Lieberman, Intermediate Schauder theory for second order parabolic equations IV. Time irregularity and regularity, Differential Integral Equations 5 (1992), 1219-1236.
  • [20] G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
  • [21] G. M. Lieberman, Time-periodic solutions of linear parabolic differential equations, Comm. Partial Differential Equations 24 (1999), 631-663.
  • [22] G. M. Lieberman, Time-periodic solutions of quasilinear parabolic differential equations I. Dirichlet boundary conditions, (to appear).
  • [23] G. M. Lieberman and N. S. Trudinger, Nonlinear oblique boundary value problems for fully nonlinear elliptic equations, Trans. Amer. Math. Soc. 295 (1986), 509-546.
  • [25] M. N. Nkashama, Semilinear periodic-parabolic equations with nonlinear boundary conditions, J. Differential Equations 130 (1996), 377-405.
  • [26] I. I. Šmulev, Periodic solutions of the first boundary value problem for parabolic equations, Mat. Sb. 66 (1965), 398-410 [Russian]; English transl. in Amer. Math. Soc. Transl. 79 (1969), 215-229.
  • [27] I. I. Šmulev, Quasi-periodic and periodic solutions of the problem with oblique derivative for parabolic equations, Differentsial'nye Uravneniya 5 (1969), 2225-2236 [Russian]; English transl. in Differential Equations 5 (1969), 2668-1676.
  • [28] N. S. Trudinger, On an interpolation inequality and its application to nonlinear elliptic equations, Proc. Amer. Math. Soc. 95 (1985), 73-78.
  • [30] N. N. Ural'tseva, Gradient estimates for solutions of nonlinear parabolic oblique boundary problems, Contemp. Math. 127 (1992), 119-130.
  • [31] O. Vejvoda, Partial differential equations: time-periodic solutions, Martinus Nijhoff, The Hague/ Boston/ London, 1982.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-bcpv52z1p163bwm
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