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Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

  • Book
  • © 2010

Overview

Authors:
  1. Thomas Lorenz

    1. Department of Mathematics, Computer Science and Mathematics, Goethe-University Frankfurt am Main, Frankfurt, Germany

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  • A broad class of evolution problems handled.
  • Each chapter is quite self-contained so that the reader can select rather freely according to the examples of 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.

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Thomas Lorenz
    Pages 1-29

  3. Extending Ordinary Differential Equations to Metric Spaces: Aubin’s Suggestion

    • Thomas Lorenz
    Pages 31-101

  4. Adapting Mutational Equations to Examples in Vector Spaces: Local Parameters of Continuity

    • Thomas Lorenz
    Pages 103-179

  5. Less Restrictive Conditions on Distance Functions: Continuity Instead of Triangle Inequality

    • Thomas Lorenz
    Pages 181-330

  6. Introducing Distribution-Like Solutions to Mutational Equations

    • Thomas Lorenz
    Pages 331-384

  7. Mutational Inclusions in Metric Spaces

    • Thomas Lorenz
    Pages 385-438

  8. Back Matter

    Pages 439-515
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Keywords

About this book

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.

Reviews

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)

“The book Mutational analysis by Thomas Lorenz is a tour de force for a young mathematician working in a new field. It is indeed an excellent, innovative and highly technical book of over 500 pages, clearly and carefully written … . this excellent book is a basic, original and very useful monograph for the development of mutational analysis both in control theory and partial differential equations.” (Jean-Pierre Aubin, Mathematical Reviews, Issue 2011 h)

Authors and Affiliations

  • Department of Mathematics, Computer Science and Mathematics, Goethe-University Frankfurt am Main, Frankfurt, Germany

    Thomas Lorenz

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