Asymptotic behaviour of linear Dirichlet parabolic problems with variable operators depending on time in varying domains
The authors consider the initial value problem for a linear parabolic problem in which the coefficients and the domain vary simultaneosly and give a generalization to the parabolic case of the results given in elliptic case by \textit{G. Dal Maso, I. V. Skrypnik} [Potential Anal. 7, No. 4, 765--803 (1997; Zbl 0887.31005)]. Substantially the authors prove that in the limit problem the H-limit of the (elliptic part of the) operator appears as well as a ``strange term'' of order zero similar to the one which appears in the elliptic case. A corrector result is also obtained. The methods are different from the ones of Dal Maso-Murat and are more similar to the methods used by the authors in [Proc. R. Soc. Edinb., Sect. A, Math. 133, 1231--1248 (2003; Zbl 1052.35017)].
scientific article; zbMATH DE number 2173099
scientific article