HUM and the wave equation with variable coefficients

Article type: Research Article

Authors: Miranda, Manuel Milla

Affiliations: Instituto de Matemática – UFRJ, C.P. 68530 – CEP 21944-970, Rio de Janeiro, RJ, Brasil

Note: [] This work was done while the author was visiting the Centre de Mathématiques Appliquées de l'École Polytechnique, France, in 1991–1992. He was partially supported by CNPq, Brazil.

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

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