11.—Equations d'Evolution du Second Ordre Associées à des Operateurs Maximaux Monotones
- 1 January 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 75 (2) , 131-147
- https://doi.org/10.1017/s0308210500017844
Abstract
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.Keywords
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