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Article

Filo, Ján
A note on asymptotic expansion for a periodic boundary condition. (English). Archivum Mathematicum, vol. 34 (1998), issue 1, pp. 83-92
MSC: 35B10, 35B27, 35C20, 35K05, 35K10 | MR 1629668 | Zbl 0911.35014
Keywords:
Heat equation; asymptotic expansion; homogenization
Summary:
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.
References:
[1] J. Bear: Hydraulics of Groundwater. McGraw-Hill, Inc. New-York 1979.
[2] H. W. Alt, S. Luckhaus: Quasilinear elliptic–parabolic differential equations. Math. Z., 183 (1983), 311-341. MR 0706391 | Zbl 0497.35049
[3] J. Filo, S. Luckhaus: Asymptotic expansion for a periodic boundary condition. J. Diff. Equations, 120 (1995), 133–173. MR 1339672 | Zbl 0849.35043
[4] S. Luckhaus, J. Filo: Asymptotic expansion for periodic boundary conditions in more space dimensions. in preparation.
[5] O. A. Ladyzenskaja V. A. Solonikov, N. N. Uralceva: Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, Vol. 23, Amer. Math. Soc., Providence, R1., 1968.
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