PROOF OF EXTENSIONS OF TWO CONJECTURES ON STRUCTURAL DAMPING FOR ELASTIC SYSTEMS

摘要: Let A (the elastic operator) be a positive, self-adjoint operator with domain D(A) in the Hubert space X, and let B dissipation another satisfying: p\Aa < p 2Aa for some constants 0 pi oo 1. Consider (corresponding to model x + Bx Ax = written as first order system), which (once closed) is plainly generator of strongly continuous semigroup contractions on E D(Aι/2) X. We prove that if 1/2 1, then such also analytic (holomorphic) triangular sector C containing positive real axis. This established fortiori two conjectures Goong Chen David L. Russell structural damping systems, referred case 1/2. Actually, special we result stronger than conjectures, yields analyticity over an explicitly identified range spaces includes E. latter was already proved our previous effort this problem. Here provide technically different simplified proof it. conceptually proofs main Finally, show not analytic.