Internal observability of the wave equation in a triangular domain

Abstract: We investigate the internal observability of the wave equation with Dirichlet boundary conditions in a triangular domain. More precisely, the domain taken into exam is the half of the equilateral triangle. Our approach is based on Fourier analysis and on tessellation theory: by means of a suitable tiling of the rectangle, we extend earlier observability results in the rectangle to the case of a triangular domain. The paper includes a general result relating problems in general domains to their tiles, and a discussion of the triangular case. As an application, we provide an estimation of the observation time when the observed domain is composed by three strips with a common side to the edges of the triangle.