Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

  • Thomas Lorenz

Part of the Lecture Notes in Mathematics book series (LNM, volume 1996)

Table of contents

About this book

Introduction

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.

Keywords

Differential equations (ordinary Distribution Evolution equations Nonsmooth analysis Set-valued dynamics Well-posed initial value problems calculus differential equation generalized) partial

Authors and affiliations

  • Thomas Lorenz
    • 1
  1. 1.Department of Mathematics, Computer Science and MathematicsGoethe-University Frankfurt am MainFrankfurtGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12471-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12470-9
  • Online ISBN 978-3-642-12471-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book