Continuity of attractors for singularly perturbed semilinear problems with nonlinear boundary conditions and large diffusion

We exhibit singularly perturbed parabolic problems with large diffusion and nonhomogeneous boundary conditions for which the asymptotic behavior can be described by a one-dimensional ordinary differential equation. We estimate the continuity of attractors in Hausdorff’s metric by the rate of convergence of resolvent operators. Moreover, we will show explicitly how this estimate of continuity varies exponentially with the fractional power spaces Xα for α in an appropriate interval.