Rate-Independent Systems

Alexander Mielke is Professor at Humboldt University of Berlin as well as a head of the research group "Partial Differential Equations" at the Weierstrass Institute for Applied Analysis and Stochastics. His research interest range over applied mathematical analysis, partial differential equations, multi-scale modeling and applications in continuum physics.Tomáš Roubíček is a Professor at Charles University in Prague, as well as a researcher at Institute of Thermomechanics and also at Institute of Information Theory and Automation of the Czech Academy of Sciences. Having an engineering background, his professional activity has evolved from computer simulations of systems of nonlinear partial differential equations thru numerical mathematics and optimization theory to applied mathematical analysis focused to mathematical modeling in engineering and physics.

• ​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​.

“The book is an interesting and useful piece of applied mathematics. It is of definite interest for researchers involved in the mathematical issues of the models in materials sciences. The book contains a clear treatment of the mathematical methods we need and a survey of many applications.” (Giuseppe Saccomands, Mathematical Reviews, July, 2016)“The book is written by two famous specialists of evolutionary systems as they worked for a long time on this topic. Throughout the whole book, the authors give lots of precise details concerning the particularities of the rate-independent systems in different and realistic settings. They take care to illustrate their theoretical notions with many examples and they complete their computations with many figures.” (Alain Brillard, zbMATH 1339.35006, 2016)“This monograph presents the research of more than one decade by the authors and their collaborators. It is strongly recommended for all scientists in the field of modeling and analyzing mechanical systems and may establish as a basic reference for further developments.” (Christian Wieners, ZAMM, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 96 (4), 2016)