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Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

Thomas Lorenz (Autor)

Buch | Softcover

XIV, 509 Seiten

2010 | 2010
Springer Berlin (Verlag)
978-3-642-12470-9 (ISBN)

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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.

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.

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.

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)

Erscheint lt. Verlag	9.6.2010
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIV, 509 p. 57 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	880 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Calculus • differential equation • Differential equations (ordinary • Distribution • Evolution Equations • generalized) • nonsmooth analysis • Ordinary differential equations • Partial • Partial differential equations • Set-valued dynamics • Well-posed initial value problems
ISBN-10	3-642-12470-4 / 3642124704
ISBN-13	978-3-642-12470-9 / 9783642124709
Zustand	Neuware