Long-time Asymptotics For The Damped Boussinesq Equation In A Disk

The paper deals with initial boundary value problem for the following equationin a unit disk. By means of applying the spectral and perturbations theories, solutions of the problem are constructed with small initial data in the form of series. The formulae for long-time asymptotics of these solutions are established. The main tool for solving the problem is Fourier-Bessel series.Some useful lemmas and results are given in Chapter 2. In Chapter 3, we solve the problem with radially symmetrical initial data and homogeneous boundary conditions. The existence of strong solutions is presented in space and the uniqueness is proved for the assumption, the uniqueness of the corresponding problem is obtained.