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- W2001919552 abstract "The Helmholtz equation with rapidly oscillating absorption coefficient and constant scattering (diffusion) coefficient is considered. It models the light absorption in a tissue containing a periodic set of thin blood vessels; it is assumed that the absorption takes place within these vessels only. So, the scattering coefficient is supposed to be constant while the absorption coefficient is equal to zero everywhere except for a periodic set of thin parallel strips simulating the blood vessels, where it is equal to the large parameter $omega$. Two other parameters appear in the problem: $varepsilon$ is the ratio of the distance between the axes of vessels to the characteristic macroscopic size, and $delta$, which is the ratio of the thickness of thin vessels and the period. Both parameters $varepsilon$ and $delta$ are small. The one-dimensional setting is considered. The classical high order homogenization method is applicable only in the case $varepsilon^2omegadeltato 0, omegadeltato infty$, while if $varepsilon^2omegadeltato const$ or $varepsilon^2omegadeltato infty$, it doesn't work and the construction of an asymptotic approximation was an open problem. Here we construct an asymptotic expansion of the solution in all three cases. Three settings are considered: in $mathbb{R}$, the periodic boundary conditions, and the Dirichlet boundary value problem." @default.
- W2001919552 created "2016-06-24" @default.
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- W2001919552 date "2012-01-01" @default.
- W2001919552 modified "2023-10-14" @default.
- W2001919552 title "Asymptotic Analysis of the One-Dimensional Diffusion-Absorption Equation with Rapidly and Strongly Oscillating Absorption Coefficient" @default.
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- W2001919552 doi "https://doi.org/10.1137/100817802" @default.
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