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• W3212940872 abstract "A general problem of current interest is the analysis of two-dimensional (2D) and three-dimensional (3D) diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One major application is to intracellular diffusion, where the holes could represent organelles or biochemical substrates. In this paper we use a combination of matched asymptotic analysis and Green's function methods to calculate the so-called accumulation time for relaxation to steady state. The standard measure of the relaxation rate is in terms of the principal nonzero eigenvalue of the negative Laplacian. However, this global measure does not account for possible differences in the relaxation rate at different spatial locations, and relies on the assumption that the eigenvalues have sufficiently large spectral gaps. As previously established for diffusion-based morphogen gradient formation, the accumulation time provides a better measure of the relaxation process." @default.
• W3212940872 created "2021-11-22" @default.
• W3212940872 creator A5013056878 @default.
• W3212940872 date "2021-11-05" @default.
• W3212940872 modified "2023-09-27" @default.
• W3212940872 title "Accumulation time of diffusion in a singularly perturbed domain" @default.
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• W3212940872 hasPublicationYear "2021" @default.
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