Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

ISBN-13: 9783642124709 / Angielski / Miękka / 2010 / 509 str.

Lorenz;¬Abar

Opis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces. .

Recenzje

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)

Spis treści

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.

O autorze

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.

Blurb

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.