Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T11:13:10.939Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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