Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T23:45:09.373Z Has data issue: false hasContentIssue false

Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries

Published online by Cambridge University Press:  22 January 2016

Yoshio Yamada*
Affiliation:
Department of Mathematics Faculty of Science, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the periodic problems for certain nonlinear parabolic differential equations in domains with periodically moving boundaries. The typical problem, which is going to be discussed in the present paper, is to solve the following:

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Benilan, P. and Brezis, H., Solutions faibles d’équations d’évolution dans les espaces de Hilbert, Ann. Inst. Fourier, Grenoble 22 (1972), 311329.CrossRefGoogle Scholar
[2] Brezis, H., Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland (1973).Google Scholar
[3] Browder, F. E. and Petryshyn, W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571575.CrossRefGoogle Scholar
[4] Fujita, H., The penalty method and some nonlinear initial value problems, Contributions to Nonlinear Functional Analysis, edited by Zarantonello, E. H., Academic Press (1971), 635665.Google Scholar
[5] Kenmochi, N., Some nonlinear parabolic variational inequalities, Israel J. Math. 22 (1975), 304331.CrossRefGoogle Scholar
[6] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars (1969).Google Scholar
[7] Nagai, T., Periodic solutions for certain time-dependent parabolic variational inequalities, Hiroshima Math. J. 5 (1975), 537549.CrossRefGoogle Scholar
[8] Yamada, Y., On evolution equations generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo 23 (1976), 491515.Google Scholar