The geometrical quantity in damped wave equations on a square
Pascal Hébrard, Emmanuel Humbert (2006)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The energy in a square membrane subject to constant viscous damping on a subset decays exponentially in time as soon as satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate of this decay satisfies (see Lebeau [ (1996) 73–109]). Here denotes the spectral abscissa of the damped wave equation operator and is a number called the geometrical quantity of and defined as follows. A ray in is the trajectory generated by the free...