Department of Mathematics2024-11-1020130362-546X10.1016/j.na.2013.04.0162-s2.0-84878257583http://dx.doi.org/10.1016/j.na.2013.04.016https://hdl.handle.net/20.500.14288/17224We obtained decay and growth estimates for solutions of second-order and third-order differential-operator equations in a Hilbert space. Applications to initial-boundary value problems for linear and nonlinear non-stationary partial differential equations modeling the strongly damped nonlinear improved Boussinesq equation, the dual-phase-lag heat conduction equations, the equation describing wave propagation in relaxing media, and the Moore-Gibson-Thompson equation are given.MathematicsApplied mathematicsJournal Article1873-5215322685300001Q13969