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  • © 2010

Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

Authors:

  • 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)

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.

Keywords

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

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

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions