A damping term for higher-order hyperbolic equations (Q268218)

Let \(Lu=0\) be a \(m\)-th-order homogeneous equation with \(L\) a strictly hyperbolic operator. This means, its symbol \(P(p,iq)\) satisfies the strict hyperbolicity condition. The goal of this paper is to prove that the operator with the symbol \(cP'(p,iq)\), \(c\) a real positive constant, is a damping term for \(L\). Actually one proves that if \(M\) denotes the operator with the symbol \(P'(p,iq)\), the solution to the equation \((L+cM)u=0\) satisfies a specific long-time decay estimate.