Sharp Estimates for the Global Attractor of Scalar Reaction–Diffusion Equations with a Wentzell Boundary Condition

In this paper, we derive optimal upper and lower bounds on the dimension of the attractor for scalar reaction–diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds on the constants involved in our asymptotic estimates, and to compare th...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 22; no. 1; pp. 85 - 106
Main Author Gal, Ciprian G.
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.02.2012
Subjects
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
35Q80
Dynamic
Maximum principle
Dynamical
35Q86
35K57
37L30
35K55
Reaction–diffusion equation
Wentzell
35B41
Finite dimension
35B40
Wentzell Laplacian
Global attractors
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Summary:In this paper, we derive optimal upper and lower bounds on the dimension of the attractor for scalar reaction–diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds on the constants involved in our asymptotic estimates, and to compare these bounds to previously known estimates for the dimension of the global attractor , K ∈{D,N,P}, of reaction–diffusion equations subject to Dirichlet, Neumann and periodic boundary conditions. The explicit estimates we obtain show that the dimension of the global attractor is of different order than the dimension of , for each K ∈{D,N,P}, in all space dimensions that are greater than or equal to three.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-011-9109-y