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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.
List of contents
Extending Ordinary Differential Equations to Metric Spaces: Aubin's Suggestion.- Adapting Mutational Equations to Examples in Vector Spaces: Local Parameters of Continuity.- Less Restrictive Conditions on Distance Functions: Continuity Instead of Triangle Inequality.- Introducing Distribution-Like Solutions to Mutational Equations.- Mutational Inclusions in Metric Spaces.
About the author
Thomas J. Lorenz, Diplom Ökonom, ist Vorstandsvorsitzender der a-m-t management performance ag und erfügt über langjährige Erfahrung im Weiterbildungssektor. Er ist Geschäftsführer einer Akademie für Weiterbildung und seit 1996 Mitglied im Vorstand des Q-Verbandes.
Summary
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.
Additional text
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)
Report
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)
