A Note on Asymptotic Expansion for a Periodic Boundary Condition

Jan Filo

Address. Institut of Applied Mathematics, Comenius University, Mlynska dolina, 842 15 Bratislava, Slovak Republic

E-mail: Jan.Filo@fmph.uniba.sk

Abstract. The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet--Neuman boundary conditions with the period going to zero in $3$D.

AMS classification. 35B27, 35C20, 35K05

Key words. Heat equation, asymptotic expansion, homogenization