Tomáš Roubíček Libros

This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigor. Then, usefulness of the abstract concepts is demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. A few other physical systems, e.g. magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are considered as well. Selected applications are accompaniedby numerical simulations illustrating both the models and the efficiency of computational algorithms. In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well written book useful. Inhaltsverzeichnis 1. A general view on rate-independent systems.- 2. Energetic rate-independent systems.- 3. Rate-independent systems in Banach spaces.- 4. Applications in continuum mechanics and physics of solids.- 5. Beyond rate independence.- Appendices.- References.- Index.

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

The series focuses on publishing high-level monographs that encompass the full range of current nonlinear analysis and its applications across various fields, including optimization, control theory, systems theory, mechanics, engineering, and other sciences. A key objective is to provide the professional community with comprehensive expositions of significant results and foundational methods that are crucial for both the theoretical and practical aspects of nonlinear analysis. Contributions that lie at the intersection of nonlinear analysis and related disciplines, encouraging further research in these areas, are especially encouraged. The editorial leadership includes Editor-in-Chief Jürgen Appell from Würzburg, Germany, along with Honorary and Advisory Editors such as Catherine Bandle, Alain Bensoussan, Avner Friedman, and Umberto Mosco. The Editorial Board features members from various global institutions, including Manuel del Pino, Mikio Kato, Wojciech Kryszewski, Vicenţiu D. Rădulescu, and Simeon Reich. Proposals for new books should be submitted to Jürgen Appell. Upcoming titles include works on elliptic and parabolic equations, functional-analytic theory of concentration compactness, and semilinear elliptic equations, reflecting the series' commitment to advancing knowledge in nonlinear analysis.