The several models of convection in a thin layer of liquid (gas) with poorly heat conducting boundaries are considered. These models demonstrate a rich dynamics of pattern formation and structural phase transitions. The primary analysis of pattern formation in such a system is performed with using of the well-studied Swift - Hohenberg model. The more advanced Proctor - Sivashinsky model is examined in order to study the second-order structural phase transitions both between patterns with translational invariance and between structures with broken translational invariance but keeping a long-range order. The spatial spectrum of arising structures and visual estimation of the number of defects are analyzed. The relation between the density of defects and the spectral characteristics of the structure is found. We also discuss the effect of noise on the formation of structural defects. It is shown that within the framework of the Proctor - Sivashinsky model with additional term, taking into account the inertial effects, the large-scale vortex structures arise as a result of the secondary modulation instability.

Nonlinear regimes of one-dimensional parametric instabilities of long-wave plasma waves are considered for the cases when the average plasma field energy density is less (Zakharov's model) or greater (Silin's model) than the plasma thermal energy. The evolution of ion energy distribution is studied.After saturation of the instability, the ion kinetic energy density normalized to the initial field energy density is found to be of the order of the ratio of linear growth rate to the plasma frequency, for the case when the initial field energy far exceeds the plasma thermal energy. In this case, the ion energy distributionis differentfrom the Maxwellian. In the opposite case of hot plasma, the ions acquire a part of initial field energy, which is approximately equal to the half of ratio of initial Langmuir field energy to the plasma thermal energy. At this, the ion kinetic energy distribution is close to the Maxwellian, and it is reasonably to speak about ion temperature. The crossing of ion trajectories in the surrounding of density cavities is a reason of instability quenching in both cases.

Конвекцію у тонкому шарі рідини (газу) між поверхнями, що недостатньо гарно проводять тепло, розглянуто за умов придатності моделі Проктора - Сівашинського, причому за відсутності залежності в'язкості від температури. З використанням числового моделювання показано, що кожний стан, можна представити фіксованим значенням функції стану, що дорівнює сумі квадратів мод просторового спектра температури на поверхні. Перехід між станами характеризується значенням похідної за часом від функції станів. Різниця між станами, що відрізняються топологією, відповідає різниці між відповідними значеннями функції станів.