Energy estimates of hyperbolic equations with dissipative lower terms (Q1103108)

A dissipative energy expression for an equation \((p(D_ x,D_ t)+q(D_ x,D_ t))u=0\) is derived where p, q are N th and (N-1) th order homogeneous t-hyperbolic polynomials with \(p(0,1)>0\), \(q(0,1)>0\) and characteristic roots of q dividing those roots of p.