Global exponential attractors for a class of almost-periodic parabolic equations in 𝑅^{𝑁}

Vuillermot, Pierre-A.

doi:10.1090/S0002-9939-1992-1102861-5

Global exponential attractors for a class of almost-periodic parabolic equations in $\textbf {R}^ N$
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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, Fisher’s 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. 5–49. 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 10–18, 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. 1, 83–98. 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. 3, 541–570. MR 1047752