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 t →C(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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ALT H.W. & LUCKHAUS S.: Quasilinear elliptic-parabolic differential equations, Math. Z. 183, 311–341 (1983)
Brezis H.: Opérateurs Maximaux Monotones, North Holland Publ. Company, Amsterdam 1973
Carstensen C. & MIELKE A.: A formulation of finite plasticity and an existence proof for one dimensional problems, preprint, If AM Univ. Hannover
Deimling K.: Nonlinear Functional Analysis, Springer, Berlin 1985
Dibenedeto E. & SHOWALTER R.E.: Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12, 731–751 (1981)
Kenmochi N. & PAWLOW I.: A class of nonlinear elliptic-parabolic equations with time-dependent constraints, Nonlinear Anal. 10, 1181–1202 (1986)
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)
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)
Kunze M. & Monteiro Marques M.D.P.: Existence of solutions for degenerate sweeping processes, to appear in J. Convex Analysis
Kunze M. & Monteiro Marques M.D.P.: On the discretization of degenerate sweeping processes, to appear in Portugaliae Mathematica
Monteiro Marques M.D.P.: Differential inclusions in nonsmooth mechanical problems-shocks and dry friction, Birkhäuser, Basel-Boston-Berlin, 1993
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Kunze, M., Monteiro Marques, M.D.P. (1999). Degenerate Sweeping Processes. In: Argoul, P., Frémond, M., Nguyen, Q.S. (eds) IUTAM Symposium on Variations of Domain and Free-Boundary Problems in Solid Mechanics. Solid Mechanics and Its Applications, vol 66. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4738-5_36
Download citation
DOI: https://doi.org/10.1007/978-94-011-4738-5_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5992-3
Online ISBN: 978-94-011-4738-5
eBook Packages: Springer Book Archive