Asymptotic Analysis - Volume 81, issue 3-4

Authors: Cardone, G. | Pastukhova, S.E. | Perugia, C.

Article Type: Research Article

Abstract: We study the homogenization of elliptic equations stated in L2 -space with degenerate weight. Both coefficients of the differential operator and the weight are ε-periodic and highly oscillating as ε tends to zero. Under minimal hypotheses on the coefficients and the weight we prove estimates of order ε and ε2 for L2 -norm of the difference between the exact solution and its appropriate approximations by L2 -norm of the right-side function. The spectral method based on Bloch decomposition is used. In the case of nonunique solution provided that the weight is not regular we consider estimates for any of …so-called variational solutions. Show more

Keywords: homogenization, spectral method, Bloch decomposition, Sobolev spaces with degenerate weight, W-solution, approximation of resolvent

DOI: 10.3233/ASY-2012-1121

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 189-209, 2013

Authors: Miara, Bernadette | Sejje Suárez, Julian

Article Type: Research Article

Abstract: We consider a three-dimensional body whose energy couples mechanic, electric and thermic effects. By using an asymptotic approach we establish the associated bi-dimensional dynamic model for a thermopiezoelectric plate. The computation of the new constitutive laws shows that pyroelectric effect (coupling of the electric field and the temperature) can appear in the limit 2D model even though the 3D dielectric displacement field does not present any coupling with the temperature. Pyrokinetic effect (coupling of elastic and temperature fields) is exhibited by the same way.

Keywords: piezoelectricity, thermopiezoelectric system, asymptotic analysis

DOI: 10.3233/ASY-2012-1126

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 211-250, 2013

Authors: Douanla, Hermann

Article Type: Research Article

Abstract: Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the solid part is positive, negative or equal to zero. We prove concise homogenization results in all three cases.

Keywords: homogenization, eigenvalue problems, perforated domains, indefinite weight function, two-scale convergence

DOI: 10.3233/ASY-2012-1127

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 251-272, 2013

Authors: Karabash, Illya M.

Article Type: Research Article

Abstract: The paper is devoted to optimization of resonances associated with 1-D wave equations in inhomogeneous media. The medium's structure is represented by a nonnegative function B. The problem is to design for a given α∈R a medium that generates a resonance on the line α+iR with a minimal possible modulus of the imaginary part. We consider an admissible family of media that arises in a problem of optimal design for photonic crystals. This admissible family is defined by the constraints 0≤b1 ≤B(x)≤b2 with certain constants b1,2 . The paper gives an accurate definition of optimal structures that ensures their …existence. We prove that optimal structures are piecewise constant functions taking only two extreme possible values b1 and b2 . This result explains an effect recently observed in numerical experiments. Then we show that intervals of constancy of an optimal structure are tied to the phase of the corresponding resonant mode and write this connection as a nonlinear eigenvalue problem. Show more

Keywords: photonic crystal, resonance perturbations, quasi-normal level

DOI: 10.3233/ASY-2012-1128

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 273-295, 2013

Authors: Conti, Monica | Dell'Oro, Filippo | Miranville, Alain

Article Type: Research Article

Abstract: We discuss the asymptotic behavior of a generalized nonlinear Caginalp phase-field system, based on the theory of heat conduction of type III devised by Green and Naghdi. In the case of two nonlinearities of polynomial critical growth, we prove the existence of global attractors of optimal regularity.

Keywords: Caginalp system, type III heat conduction, well-posedness, dissipativity, global attractor

DOI: 10.3233/ASY-2012-1129

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 297-314, 2013

Authors: Christiansen, T.J.

Article Type: Research Article

Abstract: This paper is concerned with scattering by a smooth compact obstacle in Rd . The main results are that for certain classes of obstacles knowledge of the scattering amplitude in only one or two pairs of incident and reflected directions suffices to recover the Taylor series of a boundary defining function for the obstacle at a point. Thus certain obstacles with real analytic boundaries can be determined.

Keywords: inverse problems, scattering theory, obstacle scattering, backscattering

DOI: 10.3233/ASY-2012-1130

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 315-335, 2013

Authors: Prakash, Ravi

Article Type: Research Article

Abstract: In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff–Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

Keywords: Optimal control, homogenization, Kirchhoff–Love plate, hyperbolic problem

DOI: 10.3233/ASY-2012-1132

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 337-355, 2013

Authors: Koralov, L.

Article Type: Research Article

Abstract: We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the super-critical regime, we describe the asymptotics of the number of particles in a given domain. In the sub-critical and critical regimes, we describe the distribution of the limiting number of particles.

Keywords: critical phenomena, spatial branching processes, phase transition, correlation functions

DOI: 10.3233/ASY-2012-1133

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 357-377, 2013

Article Type: Other

Citation: Asymptotic Analysis, vol. 81, no. 3-4, pp. 379-380, 2013