Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-20T02:59:21.367Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison and stability of solutions to a class of quasilinear parabolic problems

Published online by Cambridge University Press:  14 November 2011

Michel Chipot  and
José-Francisco Rodrigues
Michel Chipot
Affiliation:
Départment Mathématiques, Université de Metz, He du Saulcy, 57045 Metz Cédex, France
José-Francisco Rodrigues
Affiliation:
CMAF and University of Lisbon, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal
Get access Rights & Permissions [Opens in a new window]

Synopsis

This paper presents new comparison and uniqueness results for the solutions of parabolic quasilinear boundary value problems with (and without) obstacles. A stability result in L1(Ω) yields the asymptotic stabilisation in this space, when t → ∞) towards the corresponding elliptic problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 275 - 285
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Artola, M.. Sur une classe de problèmes paraboliques quasi-linéaires. Boll. Un. Mat. Ital. (6) 5B (1986), 51–70.Google Scholar
2Carrillo, J. and Chipot, M.. On some nonlinear elliptic equations involving derivatives of the nonlinearity. Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 281–294.Google Scholar
3Chipot, M. and Michaille, G.. Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities. (IMA Preprint #347. University of Minnesota, October 1987.)Google Scholar
4Donati, F.. A penalty method approach to strong solutions of some nonlinear parabolic unilateral problems. Nonlinear Anal. 6 (1982), 585–597.Google Scholar
5Lewy, H. and Stampacchia, G.. On existence and smoothness of solutions of some noncoercive variational inequalities. Arch. Rational Mech. Anal. 41 (1971), 241–253.CrossRefGoogle Scholar
6Lions, J. L.. Quelques-méthodes de résolution des problèmes aux limites non linéaires (Paris: Dunod, 1969).Google Scholar
7Rodrigues, J. F.. Some remarks on the asymptotic behaviour of strong solutions to monotone parabolic variational inequalities. Rend. Mat. (7) 4 (1984), 458–470.Google Scholar
8Trudinger, N. S.. On the Comparison Principle for Quasilinear Divergence Structure Equations. Arch. Rational. Mech. Anal. 57 (1974/1975), 128–133.Google Scholar