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Asymptotic Analysis - Volume 30, issue 2

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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.

Asymptotic analysis of a metallostatic pressure type boundary condition modelled by a fictitious domain method in an aluminium casting

Authors: Barral, P. | Quintela, P.

Article Type: Research Article

Abstract: In this paper we present an asymptotic analysis of the treatment of a metallostatic pressure boundary condition arising from the thermomechanical modelling of aluminium castings by means of a fictitious domain method depending on a small real parameter. We introduce an asymptotic expansion for the solution of the extended problem and we prove that the leading term of such expansion is the solution of the initial problem.

Citation: Asymptotic Analysis, vol. 30, no. 2, pp. 93-116, 2002

Price: EUR 27.50

Dirichlet boundary stabilization of the wave equation

Authors: Ammari, Kais

Article Type: Research Article

Abstract: We consider the stabilization problem for a wave equation. In the case when the geometric control assumption, see [3], is not satisfied, we prove that the energy of system decay with a logarithmic rate for all initial data in the domain of the infinitesimal generator of evolution equation. The technique used consists in deducing the decay estimate from an observability inequality for the associated undamped problem, via sharp regularity results.

Keywords: boundary stabilization, Dirichlet type boundary feedback, wave equation

Citation: Asymptotic Analysis, vol. 30, no. 2, pp. 117-130, 2002

Price: EUR 27.50

Stability of solutions to the Burgers equation

Authors: Aassila, Mohammed

Article Type: Research Article

Abstract: In this paper we study the boundary stabilization of the Burgers equation. We prove that the closed‐loop system is globally H1 ‐stable and H3 ‐stable and well‐posed. Furthermore, we show that the delayed Burgers' equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in term of the viscosity and the initial condition.

Keywords: Burgers' equation, stability, boundary control

Citation: Asymptotic Analysis, vol. 30, no. 2, pp. 131-160, 2002

Price: EUR 27.50

Weakly coupled dynamical systems and applications

Authors: Carrive, M. | Miranville, A. | Piétrus, A. | Rakotoson, J.M.

Article Type: Research Article

Abstract: In this article, we define a new class of dynamical systems that are not associated with semigroups and that we call weakly coupled systems (in the sense that the initial conditions for the different components of the system are not independent) and study the asymptotic behavior of such systems. In particular, we define and study the notions of global attractor, inertial manifold and exponential attractor associated with a weakly coupled system. We also consider the nonautonomous case. As an example, we study the asymptotic behavior of weakly coupled Cahn–Hilliard equations.

Keywords: weakly coupled system, global attractor, inertial manifold, exponential attractor, nonautonomous system, coupled Cahn–Hilliard equations

Citation: Asymptotic Analysis, vol. 30, no. 2, pp. 161-185, 2002

Price: EUR 27.50
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