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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
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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

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References

REFERENCES

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