Global exponential attractors for a class of almost-periodic parabolic equations in $\textbf {R}^ N$
HTML articles powered by AMS MathViewer
- by Pierre-A. Vuillermot PDF
- Proc. Amer. Math. Soc. 116 (1992), 775-782 Request permission
Abstract:
In this article, we construct global exponential attractors for a class of almost-periodic semilinear reaction-diffusion equations with Neumann boundary conditions on bounded regions of ${\mathbb {R}^N}$. The class of problems that we analyze here contains, in particular, Fisherโs equations of population genetics.References
- Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
- D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974) Lecture Notes in Math., Vol. 446, Springer, Berlin, 1975, pp.ย 5โ49. MR 0427837
- A. Fasano and M. Primicerio (eds.), Nonlinear diffusion problems, Lecture Notes in Mathematics, vol. 1224, Springer-Verlag, Berlin, 1986. Lectures given at the second 1985 session of the Centro Internazionale Matematico Estivo (CIME) held at Montecatini Terme, June 10โ18, 1985. MR 877985, DOI 10.1007/BFb0072686
- Paul C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics, vol. 28, Springer-Verlag, Berlin-New York, 1979. MR 527914, DOI 10.1007/978-3-642-93111-6
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
- P. Hess and H. Weinberger, Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses, J. Math. Biol. 28 (1990), no.ย 1, 83โ98. MR 1036413, DOI 10.1007/BF00171520
- B. M. Levitan and V. V. Zhikov, Almost periodic functions and differential equations, Cambridge University Press, Cambridge-New York, 1982. Translated from the Russian by L. W. Longdon. MR 690064
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
- Pierre-A. Vuillermot, Periodic soliton solutions to nonlinear Klein-Gordon equations on $\textbf {R}^2$, Differential Integral Equations 3 (1990), no.ย 3, 541โ570. MR 1047752
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 775-782
- MSC: Primary 35K55; Secondary 58F39
- DOI: https://doi.org/10.1090/S0002-9939-1992-1102861-5
- MathSciNet review: 1102861