I. Hydrodynamic Response of the Water Droplet to the Laser Irradiation. I. Electron Relaxation in the Parabolic Quantum Well.

In the first part of this thesis, method of dealing with "free boundary conditions", named "folding transformation" is devised. This method is applied to the hydrodynamical problem, solution of which involves different types of discontinuities, such as shock waves, "contact" discontinuities and "kinks". A test of the fully two-dimensional code CAVEAT for solving hydrodynamic equations is provided for the case in which external energy is deposited into the system. We show that the CAVEAT code can be successfully applied to the problems that involve an energy source. In the second part of the thesis we develop a solution of the problem of the relaxation of two-dimensional electrons confined in the parabolic well, due to the inelastic interaction with the three-dimensional phonons. We have also considered an effect of the transverse magnetic field on the electron relaxation.