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

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.

arXiv comment27 pages, to appear in Asymptotic Analysis

References in corpus (3)

• Dispersive estimates for hyperbolic systems with time-dependent coefficients
• A necessary and sufficient condition on scattering for the regularly hyperbolic systems
• Asymptotic Behaviour of Solutions to Hyperbolic Partial Differential Equations

Cited by in corpus (1)

• Data Assimilation in Large-Prandtl Rayleigh-Bénard Convection from Thermal Measurements