A Note on Homogenization of Parabolic Equation in Perforated Domains (Communications in Mathematical Research, 2019)
We are concerned with a class of parabolic equations in periodically perforateddomains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenizationresults under the conditions slightly weaker than those in the correspondingcase considered by Nandakumaran and Rajesh (Nandakumaran A K, Rajesh M. Homogenizationof a parabolic equation in perforated domain with Neumann boundarycondition. Proc. Indian Acad. Sci. (Math. Sci.), 2002, 112(1): 195–207). Moreover,these results generalize those obtained by Donato and Nabil (Donato P, Nabil A. Homogenizationand correctors for the heat equation in perforated domains. Ricerchedi Matematica L. 2001, 50: 115–144).