Mutational analysis: a joint framework for Cauchy problems in and beyond vector spaces

Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling. A broad class of evolution problems handled. Each chapter is quite self-contained so that the reader can select rather freely according to the examplesof personal interest. Each example provides a table about its main results and the underlying choice of basic sets, distances etc.- The main points of the general framework are summarized in the introduction so that the reader can get the gist quickly. INDICE: Preface Acknowledgments 0 Introduction 1 Extending ordinary differential equations to metric spaces 2 Adapting mutational equations to examples in vector space 3 Continuity of distances replaces the triangle inequality 4 Introducing distribution-like solutions to mutational equations 5 Mutational inclusions in metric spaces Tools Bibliographical Notes References Index of Notation Index

• ISBN: 978-3-642-12470-9
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 508
• Fecha Publicación: 01/06/2010
• Nº Volúmenes: 1
• Idioma: Inglés