The periodic unfolding method for perforated domains and Neumann sieve models

Unfolding-based corrector estimates for a reaction–diffusion system predicting concrete corrosion

“…Applying estimates in Lemmata 2.3, 2.5 and Convergence Theorem [7,8], see Theorem 5.3 in Appendix, implies the convergences for u ε , v ε , w ε in (12). The strong convergence of r ε is achieved by showing that T…”

“…, [7], imply the convergences of T ε Γ 1 (∂ t r ε ). To show the convergences (13), we make use of the trace theorem, [9], and of the strong convergence of T…”

Homogenization of thin piezoelectric perforated shells

“…The statement (i) is a direct consequence of (10) while (ii)-(iv) are proved in [7,9] and (v) in [7,11]. We present here only the proof of (vi).…”

Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method

“…From the mathematical point of view, the results we obtain remain true for any Ω Lipschitz open subset of R d , with appropriate boundary conditions, such as Dirichlet or Neumann's (those boundary conditions, if not scaled, should simply be added to the homogenized problems in that case, the local cell problems remaining unchanged). However, both notations and proofs are more involved when dealing with bounded domains (see [4], [5] and [6]). Thus, using R d also allow us to simplify the presentation.…”