Asymptotic Analysis - Volume 11, issue 4

Authors: Miranda, Manuel Milla

Article Type: Research Article

Abstract: This paper is concerned with the boundary exact controllability for the equation: \[w''-\sum_{i=1}^{n}\frac{\partial}{\partial x_{i}}\biggl(a_{ij}(x,t)\frac{\partial w}{\partial x_{j}}\biggr)+\sum_{i=1}^{n}b_{i}(x,t)\frac{\partial w'}{\partial x_{i}}+\sum_{i=1}^{n}d_{i}(x,t)\frac{\partial w}{\partial x_{i}}=0\quad\mbox{in}\ Q,\] where Q is a finite cylinder Ω×]0,T[, Q a bounded domain of Rn . The result is obtained by the HUM which was introduced by J.L. Lions. The above equation appears in the study of boundary exact controllability for the wave equation in non-cylindrical domains.

DOI: 10.3233/ASY-1995-11401

Citation: Asymptotic Analysis, vol. 11, no. 4, pp. 317-341, 1995

Authors: Kozlov, V.A. | Maz'ya, V.G. | Movchan, A.B.

Article Type: Research Article

Abstract: A mixed boundary value problem is posed for the Lame system in an elastic multi-structure which consists of a union of a three-dimensional domain and thin cylinders. A normalized thickness of a rod is characterized by a small parameter ε. We present a rigorous algorithm which yields a multi-scaled asymptotic expansion for the displacement and stress fields in the multi-structure. Justification of the asymptotic algorithm, including the remainder estimate for the asymptotic approximation of the displacement field, is given. The asymptotic analysis provides the range of applicability of the engineering pile structure model. It is shown that first …three eigenvalues of the spectral problem in the above multi-structure have the order O(ε4 ). The asymptotic formulae for these eigenvalues are obtained. Show more

DOI: 10.3233/ASY-1995-11402

Citation: Asymptotic Analysis, vol. 11, no. 4, pp. 343-415, 1995

Article Type: Other

Citation: Asymptotic Analysis, vol. 11, no. 4, pp. 417-417, 1995