Asymptotic expansions for high-contrast linear elasticity

Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in highcontrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the ...

Asymptotic Expansions for Integrals

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...

Asymptotic Expansions for Nonlocal Diffusion

We study the asymptotic behavior for solutions to nonlocal diffusion models of the form ut = J ∗ u − u in the whole R with an initial condition u(x, 0) = u0(x). Under suitable hypotheses on J (involving its Fourier transform) and u0, it is proved an expansion of the form ∥∥u(u)− ∑ |α|≤k (−1)|α| α! ( ∫ u0(x)x dx ) ∂Kt ∥∥ Lq(Rd) ≤ Ct−A, where Kt is the regular part of the fundamental solution and...

Strong convergence of the solutions of the linear elasticity and uniformity of asymptotic expansions in the presence of small inclusions∗

We consider the Lamé system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lamé system converge in appropriate H-norms when the shear modulus tends to infinity (the other modulus, the compressional modulus is fixed), and when the bulk modulus and the shear modulus tend to zero. Using this result, we show that the asymptotic expansion...