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Time-periodic solutions to semilinear parabolic equations

Published online by Cambridge University Press:  14 November 2011

Peter Grindrod  and
Bryan P. Rynne
Peter Grindrod
Affiliation:
Department of Mathematical Sciences, The University, Dundee DD14HN, Scotland
Bryan P. Rynne
Affiliation:
Department of Mathematical Sciences, The University, Dundee DD14HN, Scotland
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Synopsis

We consider a class of non-linear evolution equations subject to a periodic forcing term. Using bifurcation theory we obtain results on the existence and number of periodic solutions. The theory applies to semi-linear diffusion equations defined on bounded or unbounded domains.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 3-4 , 1986 , pp. 329 - 342
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Cherkas, B. M.. On Nonlinear Diffusion Equations, J. Differential Equations 11 (1972), 284–298.CrossRefGoogle Scholar
2Chow, S. N. and Hale, J. K.. Methods of Bifurcation Theory (New York: Springer, 1982).Google Scholar
3Coddington, E. A. and Levinson, N.. Theory of Ordinary Differential Equations (New York: McGraw-Hill, 1955).Google Scholar
4Fife, P. C.. Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics 28 (New York: Springer, 1979).Google Scholar
5Henry, D.. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics 840 (New York: Springer, 1981).Google Scholar
6Hille, E. and Phillips, R. S.. Functional Analysis and Semi-Groups (Providence; American Mathematical Society, 1957).Google Scholar
7Kato, T.. Perturbation Theory for Linear Operators (New York: Springer, 1976).Google Scholar
8Mizohata, S.. The Theory of Partial Differential Equations (Cambridge: Cambridge University Press, 1973).Google Scholar
9Vejvoda, O.. Partial Differential Equations: Time-periodic Solutions (The Hague: Martinus Nijhoff, 1982).Google Scholar