Average stability and decay properties of forced solutions of the wave propagation problems of classical physics in energy and mean norms (Q910548)

It is considered the wave propagation problem of classical physics as described by \[ \partial u/\partial t=E(x,t)^{-1}\sum^{n}_{1}A_ j(\partial u/\partial x_ j)+B(x,t)u+\lambda u+f(x,t). \] The paper considers several cases of this problem; the local energy, eventual local energy and the global energy are defined and their estimates obtained.