Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T19:30:09.187Z Has data issue: false hasContentIssue false
  • English
  • Français

11.—Equations d'Evolution du Second Ordre Associées à des Operateurs Maximaux Monotones

Published online by Cambridge University Press:  14 February 2012

Laurent Véron
Laurent Véron
Affiliation:
Faculté des Sciences (Mathématiques), Université de Tours
Get access Rights & Permissions [Opens in a new window]

Synopsis

This paper extends some recent results of V. Barbu and H. Brézis. It is concerned with bounded solutions of the problem pu″+qu′ ∈ Au, u(0) = a, where A is a maximal monotone operator in a real Hilbert space H and p and q are real functions. Existence and uniqueness theorems are proved, with results on integrability of solutions in various measure spaces on R+. T(t) denotes the family of contractions of D(A) generated by the equation and we obtain a regularising effect on the initial data. Some properties of this family of contractions are studied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 2 , 1976 , pp. 131 - 147
Copyright
Copyright © Royal Society of Edinburgh 1976

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

REFERENCES

1Barbu, V.. A class of boundary value problems for second order abstract differential equations. Fac. Sci. Univ. Tokyo, Sect. 1 A Math. 19 (1972), 295–319.Google Scholar
2Bourbaki, N.. Integration, 2e édn. (Paris: Hermann, 1965).Google Scholar
3Brézis, H.. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert (Amsterdam: North-Holland, 1973).Google Scholar
4Brézis, H.. Equations d'évolution du second ordre associées à des opérateurs monotones. Israel J. Math. 12 (1972), 51–60.CrossRefGoogle Scholar
5Brézis, H.. Propriétés régularisantes de certains semi-groupes non linéaires. Israel J. Math. 9 (1971), 513–534.CrossRefGoogle Scholar
6Brézis, H.. Monotonicity methods. In Contributions to nonlinear functional analysis: Proceedings of a symposium conducted by the Mathematics Research Center, University of Wisconsin, Madison, April 12–14, 1971 (London: Academic Press, 1971).Google Scholar
7Brézis, D.. Interpolation et opérateurs non linéaires. Thèe Université Paris VI, 1974.Google Scholar
8Butzer, P. L. and Bérens, H.. Semi-groups of operators and approximation (Berlin: Springer, 1967).CrossRefGoogle Scholar
9Lions, J. L.. Problèmes aux limites dans les équations aux dérivées partielles (Montreal: Presses de l'Université, 1965).Google Scholar
10Pavel, N.. Non linear boundary value problems for second order differential equations. J. Math. Anal. Appl. 50 (1975), 373–383.CrossRefGoogle Scholar
11Véron, L.. Problèmes d'évolution du second ordre associés à des opérateurs monotones. C.R. Acad. Sci. Paris Sér A-B, 278 (1974), 1099–1101.Google Scholar