We study a family of semilinear reaction-diffusion equations on spatial domains ${\Omega }_{\epsilon }$, ε > 0, in ${ℝ}^l$ lying close to a k-dimensional submanifold ℳ of ${ℝ}^l$. As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by $H{¹}_s\left(\Omega \right)$. The definition of $H{¹}_s\left(\Omega \right)$, given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...