In this paper we study the homogenization of the linear equation R(ε(-1)x) &PARTIAL; u(ε)/&PARTIAL; t - div(a(ε(-1)x) (.) &DEL; u(ε)) = f, with appropriate initial/final conditions, where R is a measurable bounded periodic function and a is a bounded uniformly elliptic matrix, whose coefficients a(ij) are measurable periodic functions. Since we admit that R may vanish and change sign, the usual compactness of the solutions in L-2 may not hold if the mean value of R is zero.
Homogenization of changing-type evolution equations
PARONETTO, FABIO
2005
Abstract
In this paper we study the homogenization of the linear equation R(ε(-1)x) &PARTIAL; u(ε)/&PARTIAL; t - div(a(ε(-1)x) (.) &DEL; u(ε)) = f, with appropriate initial/final conditions, where R is a measurable bounded periodic function and a is a bounded uniformly elliptic matrix, whose coefficients a(ij) are measurable periodic functions. Since we admit that R may vanish and change sign, the usual compactness of the solutions in L-2 may not hold if the mean value of R is zero.File in questo prodotto:
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