Asymptotic Analysis - Volume 39, issue 2

Authors: Spagnuolo, Anna Maria | Wright, Steve

Article Type: Research Article

Abstract: A derivation of a multiple‐porosity model for the flow of a single‐phase, slightly compressible fluid in a multiscale, naturally‐fractured reservoir is presented using recursive homogenization theory. The model was rigorously derived by the authors under different assumptions on the flow in relation to the geometry of the medium. In the earlier work, a recursive assumption on the flow at each level was made in order to treat certain internal boundary conditions. In the present work, the model is derived using reasonable assumptions for the geometry of the medium as well as the physics of the flow.

Keywords: naturally‐fractured media, multiple‐porosity model, fissures, homogenization

Citation: Asymptotic Analysis, vol. 39, no. 2, pp. 91-112, 2004

Authors: Ansini, Nadia

Article Type: Research Article

Abstract: We consider variational problems defined on domains ‘weakly’ connected through a separation hyperplane (‘sieve plane’) by an ε‐periodically distributed ‘contact zone’. We study the asymptotic behaviour as ε tends to 0 of integral functionals in such domains in the nonlinear and vector‐valued case, showing that the asymptotic memory of the sieve is described by a nonlinear ‘capacitary‐type’ formula. In particular we treat the case when the integral energies on both sides of the sieve plane satisfy different growth conditions. We also study the case of thin films, with flat profile and thickness ε, connected by the same sieve plane.

Keywords: sieve problem, nonlinear capacity, thin films, $\varGamma$‐limits

Citation: Asymptotic Analysis, vol. 39, no. 2, pp. 113-145, 2004

Authors: Hoang, Viet Ha

Article Type: Research Article

Abstract: The paper considers a diffusion equation in a thin domain of thickness ε in $\mathbb{R}^{n}$ whose diffusivity varies periodically with a period cell of size εp (p>0) in the cross section. The domain is highly heterogeneous so that the diffusivity is of the scale εα (α>0) in a part of the period cell and is of order 1 in the rest. The asymptotic behaviour of the solution when ε→0 is studied for all the values of p and α. In some cases, the limiting equation is in $\mathbb{R}^{n-1}$ as in the previous works on …diffusion in thin domains but in some others, an equation in $\mathbb{R}^{n}$ is obtained. Show more

Citation: Asymptotic Analysis, vol. 39, no. 2, pp. 147-167, 2004

Authors: Maz'ya, V. | Slutskiǐ, A.S.

Article Type: Research Article

Abstract: The Dirichlet problem for a quasilinear elliptic equation of the second order with quadratic nonlinearity in the first derivatives is considered in a plane domain with a corner point. An asymptotic solution which has a strong singularity at this point is constructed.

Keywords: quasilinear elliptic equations, asymptotic solutions, corner boundary points

Citation: Asymptotic Analysis, vol. 39, no. 2, pp. 169-185, 2004