Asymptotic Analysis - Volume 3, issue 3

Authors: Carlsson, Ulf

Article Type: Research Article

DOI: 10.3233/ASY-1990-3301

Citation: Asymptotic Analysis, vol. 3, no. 3, pp. 189-214, 1990

Authors: Chemin, J.Y.

Article Type: Research Article

Abstract: After the statement of a local existence theorem for compressible Euler systems, we prove, under the assumption of existence of a smooth global solution, an asymptotic estimate for internal energy. As a corollary, we obtain a result of nonglobal existence of a smooth solution in one space dimension.

DOI: 10.3233/ASY-1990-3302

Citation: Asymptotic Analysis, vol. 3, no. 3, pp. 215-220, 1990

Authors: Defranceschi, Anneliese

Article Type: Research Article

Abstract: By means of the notion of G-convergence introduced in [4] we deal with the limit behaviour, as h→+∞, of the solutions uh to Neumann boundary value problems for quasi-linear monotone operators of the form Ah u=−div(ah (x,Duh )), and we also include in our analysis more general linear boundary conditions. Furthermore, we extend the homogenization result obtained in [6] to this case and the corresponding correctors studied in [7]. Finally, we deal with the asymptotic behaviour, as h→+∞, of the solutions uh to quasi-linear equations −div(ah (x,Duh ))=f on perforated domains Ωh ⊆Ω of Rn with homogeneous …Neumann boundary conditions on the holes, when the regularity assumptions on ah required in [5] are dropped. Show more

DOI: 10.3233/ASY-1990-3303

Citation: Asymptotic Analysis, vol. 3, no. 3, pp. 221-247, 1990

Authors: Colli, Pierluigi | Rodrigues, José-Francisco

Article Type: Research Article

Abstract: We study the asymptotic behaviour of the diffusion-transmission problem in a fixed domain surrounded by a layer whose thickness of order δ goes to zero and where the specific heat σ goes to infinity. We characterize essentially three limit cases according to the limit α of the product δσ: if α=0 or α=∞, we have a Neumann or a Dirichlet boundary condition respectively, while if 0<α<∞, we obtain a mixed boundary condition involving the trace of the time derivative. We also extend this result to a class of unilateral problems of Signorini type.

DOI: 10.3233/ASY-1990-3304

Citation: Asymptotic Analysis, vol. 3, no. 3, pp. 249-263, 1990