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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 AW for scalar reaction-diffusion equations with a Wentzell
(dynamic) boundary condition. We are also interested in obtaining explicit
bounds about the constants involved in our asymptotic estimates, and to compare
these bounds to previously known estimates for the dimension of the global
attractor AK; K \in {D;N; P}, of reactiondiffusion equations subject to
Dirichlet, Neumann and periodic boundary conditions. The explicit estimates we
obtain show that the dimension of the global attractor AW is of different order
than the dimension of AK; for each K \in {D;N; P} ; in all space dimensions
that are greater or equal than three.Comment: to appear in J. Nonlinear Scienc
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