Advertisement

Degenerate Sweeping Processes

  • M. Kunze
  • M. D. P. Monteiro Marques
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)

Abstract

The aim of this paper is to summarize some recent results concerning the evolutionary differential inclusions {fy(1)|31-1} where A is a maximal monotone and strongly monotone operator in a real Hilbert space H, and tC(t) is a set-valued mapping, cf. the precise assumptions below. Moreover, as usually, denotes the cone of normals to the closed convex set C(t) at the point v G C(t).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    ALT H.W. & LUCKHAUS S.: Quasilinear elliptic-parabolic differential equations, Math. Z. 183, 311–341 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brezis H.: Opérateurs Maximaux Monotones, North Holland Publ. Company, Amsterdam 1973zbMATHGoogle Scholar
  3. 3.
    Carstensen C. & MIELKE A.: A formulation of finite plasticity and an existence proof for one dimensional problems, preprint, If AM Univ. HannoverGoogle Scholar
  4. 4.
    Deimling K.: Nonlinear Functional Analysis, Springer, Berlin 1985CrossRefzbMATHGoogle Scholar
  5. 5.
    Dibenedeto E. & SHOWALTER R.E.: Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12, 731–751 (1981)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kenmochi N. & PAWLOW I.: A class of nonlinear elliptic-parabolic equations with time-dependent constraints, Nonlinear Anal. 10, 1181–1202 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kröner D.: Parabolic regularization and behaviour of the free boundary for un-saturated flow in a porous medium, J. Reine Angew. Math. 348, 180–196 (1984)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Kröner D. & Rodrigues J.F.: Global behaviour for bounded solutions of a porous media equation of elliptic-parabolic type, J. de Mathématique pures et appliquées 64, 105–120 (1985)zbMATHGoogle Scholar
  9. 9.
    Kunze M. & Monteiro Marques M.D.P.: Existence of solutions for degenerate sweeping processes, to appear in J. Convex Analysis Google Scholar
  10. 10.
    Kunze M. & Monteiro Marques M.D.P.: On the discretization of degenerate sweeping processes, to appear in Portugaliae Mathematica Google Scholar
  11. 11.
    Monteiro Marques M.D.P.: Differential inclusions in nonsmooth mechanical problems-shocks and dry friction, Birkhäuser, Basel-Boston-Berlin, 1993CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • M. Kunze
    • 1
  • M. D. P. Monteiro Marques
    • 2
  1. 1.Mathematische Institut der Universität Köln;KölnGermany
  2. 2.C.M.A.F. and Faculdade de Ciências da Universidade de LisboaLisboaPortugal

Personalised recommendations