Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients

Article type: Research Article

Authors: Yamazaki, Taeko

Affiliations: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan. E-mail: yamazaki_taeko@ma.noda.tus.ac.jp

Abstract: This paper is concerned with an abstract dissipative hyperbolic equation with time-dependent coefficient. Under an assumption which ensures that the energy does not decay, this paper provides a condition on the coefficient, which is necessary and sufficient so that the solutions tend to the solutions of the free wave equation.

Keywords: abstract linear hyperbolic equation, asymptotic behavior, asymptotically free property

DOI: 10.3233/ASY-151354

Journal: Asymptotic Analysis, vol. 97, no. 1-2, pp. 165-187, 2016