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1996-1997 | 24 | 1 | 97-107
Tytuł artykułu

On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.
Rocznik
Tom
24
Numer
1
Strony
97-107
Opis fizyczny
Daty
wydano
1996
otrzymano
1996-01-26
Twórcy
  • Mathematical Institute, Academy of Sciences, Žitná 25, CZ-115 67 Praha 1, Czech Republic
autor
  • Mathematical Institute, Academy of Sciences, Žitná 25, CZ-115 67 Praha 1, Czech Republic
Bibliografia
  • [1] L. Boccardo, T. Gallouët et F. Murat, Unicité de la solution de certaines équations elliptiques non linéaires, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 1159-1164.
  • [2] L. Čermák and M. Zlámal, Transformation of dependent variables and the finite element solution of nonlinear evolution equations, Internat. J. Numer. Methods Engrg. 15 (1980), 31-40.
  • [3] P. Doktor, On the density of smooth functions in certain subspaces of Sobolev spaces, Comment. Math. Univ. Carolin. 14 (1973), 609-622.
  • [4] J. Douglas and T. Dupont, A Galerkin method for a nonlinear Dirichlet problem, Math. Comp. 29 (1975), 689-696.
  • [5] J. Douglas, T. Dupont and J. Serrin, Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form, Arch. Rational Mech. Anal. 42 (1971), 157-168.
  • [6] M. Feistauer, M. Křížek and V. Sobotíková, An analysis of finite element variational crimes for a nonlinear elliptic problem of a nonmonotone type, East-West J. Numer. Math. 1 (1993), 267-285.
  • [7] M. Feistauer and A. Ženíšek, Compactness method in finite element theory of nonlinear elliptic problems, Numer. Math. 52 (1988), 147-163.
  • [8] J. Franců, Monotone operators. A survey directed to applications to differential equations, Appl. Math. 35 (1990), 257-301.
  • [9] H. Gajewski, K. Gröger and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.
  • [10] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
  • [11] R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer, New York, 1984.
  • [12] I. Hlaváček and M. Křížek, On a nonpotential and nonmonotone second order elliptic problem with mixed boundary conditions, Stability Appl. Anal. Contin. Media 3 (1993), 85-97.
  • [13] I. Hlaváček, M. Křížek and J. Malý, On Galerkin approximations of quasilinear nonpotential elliptic problem of a nonmonotone type, J. Math. Anal. Appl. 184 (1994), 168-189.
  • [14] R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal. 101 (1988), 1-27.
  • [15] M. Křížek and Q. Lin, On diagonal dominance of stiffness matrices in 3D, East-West J. Numer. Math. 3 (1995), 59-69.
  • [16] M. Křížek and P. Neittaanmäki, Mathematical and Numerical Modelling in Electrical Engineering: Theory and Applications, Kluwer, Amsterdam, 1996.
  • [17] S. Larsson, V. Thomée and N. Y. Zhang, Interpolation of coefficients and transformation of the dependent variable in the finite element methods for the nonlinear heat equation, Math. Methods Appl. Sci. 11 (1989), 105-124.
  • [18] N. G. Meyers, An example of non-uniqueness in the theory of quasi-linear elliptic equations of second order, Arch. Rational Mech. Anal. 14 (1963), 177-179.
  • [19] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967.
  • [20] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Teubner, Leipzig, 1983.
  • [21] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1967.
  • [22] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
  • [23] J. Serrin, On the strong maximum principle for quasilinear second order differential inequalities, J. Funct. Anal. 5 (1970), 184-193.
  • [24] A. Ženíšek, Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations, Academic Press, London, 1990.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i1p97bwm
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