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On a class of evolution problems

Published online by Cambridge University Press:  14 November 2011

Gaetano Fichera
Gaetano Fichera
Affiliation:
University of Rome, Rome, Italy
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Synopsis

A class of evolution problems is investigated [see (1.5), (1.6), (1.7) of the present paper] which includes, as a particular case, an evolution problem previously considered by a different author. Existence and uniqueness theorems are given in several function spaces. It is shown that, when the solution is required to belong to spaces of smooth functions, the problem becomes overdetermined. The necessary and sufficient integro-differential equations, to be satisfied by the datum, for the existence of a smooth solution, are given.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 247 - 256
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Sauer, N.. Linear evolution equations in two Banach spaces. Proc. Roy. Soc. Edinburgh Sect. A 91 (1982), 287–303.Google Scholar
2Fichera, G.. Existence Theorems in Elasticity. Handbuch der Physik, vol. VI a/2, 347–389 (Berlin: Springer, 1972).Google Scholar
3Fichera, G.. Linear elliptic differential systems and eigenvalue problems. Lecture Notes in Mathematics 8 (Berlin: Springer, 1965).Google Scholar
4Nádai, A.. Die Elastischen Platten (Berlin: Springer, 1925).Google Scholar
5Weinstein, A.. Etude des spectres des équations aux dérivées partielles de la théorie des plaques élastiques. Mém. des Sci. Math. fasc. 88 (Paris: Gauthier-Villars, 1937).Google Scholar
6Gould, S. H.. Variational Methods for Eigenvalue Problems, 2nd edn (Univ. of Toronto Press, 1966).CrossRefGoogle Scholar
7Weinstein, A. and Stenger, W.. Methods of Intermediate Problems for Eigenvalues (New York: Academic Press, 1972).Google Scholar