Asymptotic Analysis - Volume 101, issue 1-2

Authors: Goffi, F.Z. | Lemrabet, K. | Laadj, T.

Article Type: Research Article

Abstract: We consider the diffraction of time-harmonic electromagnetic waves by a perfectly conducting planar obstacle, coated by thin contrasted multi-layers of dielectric materials. A partial Fourier transform is used to derive an impedance condition that links the tangential components of the electric and magnetic fields, and transfers the boundary condition from the obstacle’s face to the other face of dielectric multi-layers. We first determine the exact formula and construct approximations of the impedance condition for one dielectric thin layer; after that, we extend the obtained result to multi-layers.

Keywords: Time-harmonic Maxwell’s system, scattering, thin dielectric layers, impedance operator

DOI: 10.3233/ASY-161391

Citation: Asymptotic Analysis, vol. 101, no. 1-2, pp. 1-15, 2017

Authors: Assal, Marouane

Article Type: Research Article

Abstract: In the Heisenberg picture, we study the semiclassical time evolution of a bounded quantum observable Q w ( x , ℏ D x ; ℏ ) associated to a ( m × m ) matrix-valued symbol Q generated by a semiclassical matrix-valued Hamiltonian H ∼ H 0 + ℏ H 1 . Under a non-crossing assumption on the eigenvalues of the principal symbol H 0 that ensures the existence of almost invariant subspaces …of L 2 ( R n ) ⊗ C m , and for a class of observables that are semiclassically block-diagonal with respect to the projections onto these almost invariants subspaces, we establish a long time matrix-valued version for the semiclassical Egorov theorem valid in a large time interval of Ehrenfest type T ( ℏ ) ≃ log ( ℏ − 1 ) . Show more

Keywords: Egorov theorem, quantum evolution, semiclassical approximation, ℏ-pseudodifferential systems

DOI: 10.3233/ASY-161394

Citation: Asymptotic Analysis, vol. 101, no. 1-2, pp. 17-67, 2017

Authors: Abdelhedi, Bouthaina

Article Type: Research Article

Abstract: We consider the second grade fluid equations on a thin three-dimensional domain with periodic boundary conditions. We prove global existence and uniqueness of the solution for large initial data. We use an appropriate decomposition of solution u into a v part, which is solution of a 2 D second grade fluid equations and the remaining w part which has an initial data converging to 0 as the thickness of the thin domain goes to 0.

Keywords: Second grade fluid equations, thin domains, perturbation, global existence

DOI: 10.3233/ASY-161397

Citation: Asymptotic Analysis, vol. 101, no. 1-2, pp. 69-95, 2017