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Asymptotic Analysis - Volume 73, issue 3

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Stabilization of a piezoelectric system

Authors: Ammari, Kaïs | Nicaise, Serge

Article Type: Research Article

Abstract: We consider a stabilization problem for a piezoelectric system. We prove an exponential stability result under some Lions geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate observability estimate.

Keywords: elasticity system, Maxwell's system, piezoelectric system, stabilization

DOI: 10.3233/ASY-2011-1033

Citation: Asymptotic Analysis, vol. 73, no. 3, pp. 125-146, 2011

Price: EUR 27.50

Limit cases in an elliptic problem with a parameter-dependent boundary condition

Authors: García-Melián, Jorge | Rossi, Julio D. | Sabina de Lis, José C.

Article Type: Research Article

Abstract: In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem  −Δp u+a(x)up−1 =−ur  in Ω,  |∇u|p−2  ∂u/∂ν=λup−1  on ∂Ω for λ∈R, where r>p−1>0, a∈L∞ (Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determine their asymptotic behavior both when r→p−1 and when r→∞.

Keywords: linear and nonlinear eigenvalue problems, sub- and super-solutions, variational methods

DOI: 10.3233/ASY-2011-1035

Citation: Asymptotic Analysis, vol. 73, no. 3, pp. 147-168, 2011

Price: EUR 27.50

Eigenvalue asymptotics for a star-graph damped vibrations problem

Authors: Pivovarchik, Vyacheslav | Woracek, Harald

Article Type: Research Article

Abstract: We consider a boundary value problem generated by Sturm–Liouville equations on the edges of a star-shaped graph. Thereby a continuity condition and a condition depending on the spectral parameter is imposed at the interior vertex, corresponding to the case of damping in the problem of small transversal vibrations of a star graph of smooth inhomogeneous strings. At the pendant vertices Dirichlet boundary conditions are imposed. We describe the eigenvalue asymptotics of the problem under consideration.

Keywords: eigenvalue asymptotics, Sturm–Liouville theory, star-graph, Kirchhoff condition

DOI: 10.3233/ASY-2011-1040

Citation: Asymptotic Analysis, vol. 73, no. 3, pp. 169-185, 2011

Price: EUR 27.50
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