Vladimirov V. Nonlinear wave structures in relaxing media models

The dissertation is devoted to construction and investigation of continual models of media with hierarchic structure. There are obtained dynamical equations of state, describing the structure manifestation on macrolevel. Conditions, leading to the autowave regimes appearance are found. There are located domains of parameter space, corresponding to the multiperiodic, quasiperiodic and chaotic regimes. Peculiarities of strange attractors, corresponding to different kinds of nonlocalities, are studied. There are performed numerical simulations of the hydrodynamic model of structured medium and stated that invariant autowave solutions play role of intermediate asymptotics for a wide class of Cauchy and boundary value problems. For the hydrodynamic models without relaxation symmetry analysis is performed and exact solutions are found. For the Tate equation of state non-local change of variables is obtained, leading to the linear equation