Asymptotic Analysis - Volume 100, issue 3-4

Authors: Azouz, Salima | Guesmia, Senoussi

Article Type: Research Article

Abstract: In this work we construct an asymptotic expansion to the weak solution of anisotropic singular perturbation problems of elliptic type. The paper aims to go deep in the study of the rate of convergence. In fact the analysis of the asymptotic expansion strongly helps in understanding what is, and what is not, needed to improve the rate and the type of convergence. In order to define the coefficients of the development some smoothness basic properties (with respect to the parameters) of elliptic problems are established.

Keywords: Singular perturbations, asymptotic development, anisotropic, elliptic problems, regularity of solutions

DOI: 10.3233/ASY-161389

Citation: Asymptotic Analysis, vol. 100, no. 3-4, pp. 131-152, 2016

Authors: Charve, Frédéric

Article Type: Research Article

Abstract: In the present article we consider a capillary compressible system introduced by C. Rohde after works of Bandon, Lin and Rogers, called the order-parameter model, and whose aim is to reduce the numerical difficulties generated by the classical local Korteweg system (involving derivatives of order three) or the non-local system (also introduced by Rohde after works of Van der Waals, and which involves a convolution operator). We prove that this system has a unique global solution for initial data close to an equilibrium and we obtain the convergence of this solution towards the local Korteweg model as well as a …convergence rate with respect to the order parameter, in accordance to what conjectured C. Rohde. As a by-product, the a priori estimates we obtain allow to provide global existence results in the L p setting (p ≠ 2 ). Show more

Keywords: Compressible Navier–Stokes system, local and non-local capillarity, Besov spaces, Lagrangian change of variables

DOI: 10.3233/ASY-161390

Citation: Asymptotic Analysis, vol. 100, no. 3-4, pp. 153-191, 2016

Authors: Boulaaras, Salah

Article Type: Research Article

Abstract: The main purpose of this paper is to analyze the convergence and regularity of the proposed algorithm (J. Nonlinear Sci. Appl. 9 (2016 ), 568–583) of the discontinuous Galerkin methods coupled with Euler time discretization scheme for parabolic quasi-variational inequalities with nonlinear source terms and an obstacle defined as impulse control problem.

Keywords: Finite elements, Euler scheme, fixed point, PQVIs, EQVIs, geometric convergence

DOI: 10.3233/ASY-161392

Citation: Asymptotic Analysis, vol. 100, no. 3-4, pp. 193-208, 2016

Authors: Hajaiej, Hichem | Molica Bisci, Giovanni | Vilasi, Luca

Article Type: Research Article

Abstract: We are concerned with existence results for a critical problem of Brézis–Nirenberg-type driven by an integro-differential operator of fractional nature. The latter includes, for a specific choice of the kernel, the usual fractional Laplacian. Under mild assumptions on the subcritical part of the nonlinearity, we provide first the existence of one weak solution through direct minimization of the energy in a small ball of a certain fractional Sobolev space. This approach remains still valid when adding small singular terms. We finally show that for appropriate choices of the parameters involved the mountain-pass approach is also applicable and yields another existence …result. Show more

Keywords: Critical nonlinearities, singular nonlinearities, integro-differential operators, fractional Laplacian, existence

DOI: 10.3233/ASY-161393

Citation: Asymptotic Analysis, vol. 100, no. 3-4, pp. 209-225, 2016

Article Type: Other

Citation: Asymptotic Analysis, vol. 100, no. 3-4, pp. 227-227, 2016