In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Focusing on infinite dimensional dynamical systems, this book explores those generated by dissipative partial differential equations, which are significant in mechanics, physics, and various scientific fields. It offers a systematic analysis of these systems, addressing their complexities and applications. The second edition features updates and extensions, enhancing its relevance for researchers and practitioners in the field.
The book explores advanced concepts in fluid dynamics and related fields, covering topics such as viscous flow and magnetohydrodynamics. It delves into atmospheric flows and the behavior of shock equations, while also addressing turbulence and nonlinear solid mechanics. Additionally, the text discusses solitons, providing a comprehensive overview of these complex subjects for readers interested in the interplay between fluid dynamics and other physical phenomena.
This study of the problem of the equilibrium of a perfectly plastic body under specific conditions employs tools and methods that can be applied to other areas, including the mechanics of fracture and certain optimal control problems. The three-part approach begins with an exploration of variational problems in plasticity theory, covering function spaces, concepts and results of convex analysis, formulation and duality of variational problems, limit analysis, and relaxation of the boundary condition. The second part examines the solution of variational problems in the finite-energy spaces; its topics include relaxation of the strain problem, duality between the generalized stresses and strains, and the existence of solutions to the generalized strain problem. The third and final part addresses asymptotic problems and problems in the theory of plates. The text includes a substantial bibliography and a new Preface and appendix by the author.