PDEs in Moving Time Dependent Domains
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a particular case of par
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Ramon G. Rubio · Yuri S. Ryazantsev Victor M. Starov · Guo-Xiang Huang Alexander P. Chetverikov · Paolo Arena Alex A. Nepomnyashchy · Alberto Ferrus Eugene G. Morozov Editors
Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics
Springer Complexity Springer Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systems – cutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science. Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse “real-life” situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications. Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence. The three major book publication platforms of the Springer Complexity program are the monograph series “Understanding Complex Systems” focusing on the various applications of complexity, the “Springer Series in Synergetics”, which is devoted to the quantitative theoretical and methodological foundations, and the “SpringerBriefs in Complexity” which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works.
Editorial and Programme Advisory Board Henry Abarbanel, Institute for Nonlinear Science, University of California, San Diego, USA Dan Braha, New England Complex Systems Institute and University of Massachusetts Dartmouth, USA ´ P´eter Erdi, Center for Complex Systems Studies, Kalamazoo College, USA and Hungarian Academy of Sciences, Budapest, Hungary Karl Friston, Institute of Cognitive Neuroscience, University College London, London, UK Hermann Haken, Center of Synergetics, University of Stuttgart, Stuttgart, Germany Viktor Jirsa, Centre National de la Recherche Scientifique (CNRS), Universit´e de la M´editerran´ee, Marseille, France Janusz Kacprzyk, System Research, Polish Academy of Sciences, Warsaw, Poland Kunihiko Kaneko, Research Center for Complex Systems Biology, The Universi
