Synopses & Reviews
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.
Review
From the reviews: "This monograph contains bibliographical notes, references, index of notations and index. In short the entire monograph is written clearly ... . This monograph is suitable for graduate students and researchers in this field." (Seenith Sivasundaram, Zentralblatt MATH, Vol. 1198, 2010)
Synopsis
Ordinary differential equations have been extended to evolution equations in Banach spaces. 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.
Table of Contents
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