Hyperbolic hydrodynamics with memory. Models and solutions. On the memory of V. A. Danylenko, who was the initiator of investigations

      Аннотация: This book considers the solutions of the generalized mathematical models providing the description of complex nonequilibrium media and their self-organized states. To develop the models, it is used the concept of generalized continuum mechanics and relaxation formalism leading to the hyperbolic extensions of parabolic classic equations, generalized hydrodynamics and hierarchically composed systems. The authors mainly focus on the travelling wave solutions which were shown to describe periodic, multiperiodic, quasiperiodic, chaotic and solitary regimes of system’s evolution. Moreover, the exotic solutions (e. i. blow-up modes, solutions with finite supports), bifurcations, evolution of initial disturbances, multidimensional phenomena of structures formation are discussed as well. The methods of studies are based on the symmetry of differential equations, qualitative, numerical and functional analysis and aim to show the general properties of models and their solutions avoiding exhausting analytical calculations and numerical details. The book addresses the researches in the fields of dynamics of complex media. It also can be used during preparation of advanced courses.

Ключевые слова: Chaos, Travelling Waves, blow-ups, collapses, hyperbolic heat and FitzHugh-Nagumo equations, generalized hydrodynamics, homoclinic existence, compactons, Bifurcations, Self-Organization