Asymptotic Analysis - Volume 19, issue 1

Authors: Martinez, Patrick

Article Type: Research Article

Abstract: We consider the system of the wave equation with the Dirichlet boundary condition damped with a local linear dissipation of the type a(x)u' . In order to simplify, we assume that the domain is the open ball of \mathbf{R}^N centered in O and of radius R and that the function a is radial near the boundary. When a goes quickly to zero at the boundary, we obtain a precise decay rate estimate of the energy of the solutions. This extends some results of Zuazua and Nakao. The proof is …based on a new nonlinear integral inequality and on the asymptotic behavior of the function a at the boundary. Show more

Citation: Asymptotic Analysis, vol. 19, no. 1, pp. 1-17, 1999

Authors: Sili, A.

Article Type: Research Article

Abstract: We consider a vectorial monotone problem posed on a cylinder {\varOmega}^\varepsilon=\omega\times (0,\varepsilon L) of \mathbb{R}^N and we study its limit behavior as \varepsilon goes to 0 . We show that the limit solution solves an elliptic system posed on \omega . We give also a corrector result as well as an error estimate under some regularity hypotheses.

Citation: Asymptotic Analysis, vol. 19, no. 1, pp. 19-33, 1999

Authors: Andreoiu‐Banica, Georgiana

Article Type: Research Article

Abstract: We apply the method of asymptotic expansions with the thickness as the small parameter to the three‐dimensional shallow shell problem of Marguerre–von Kármán written in curvilinear coordinates, with the displacement as the unknown. We prove that the leading term of the asymptotic expansion can be identified with the solution of a two‐dimensional problem. We also establish the existence and regularity of solutions to this two‐dimensional problem.

Citation: Asymptotic Analysis, vol. 19, no. 1, pp. 35-55, 1999

Authors: Kozlov, Vladimir | Maz’ya, Vladimir

Article Type: Research Article

Abstract: A two‐dimensional Riccati’s equation with Neumann boundary data is considered in a domain with an angular point. Asymptotic formulas for an arbitrary solution near the vertex are obtained.

Citation: Asymptotic Analysis, vol. 19, no. 1, pp. 57-79, 1999