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Other titles in the Lecture Notes in Mathematics series:

Lecture Notes in Mathematics #1996: Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

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Lecture Notes in Mathematics #1996: Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Ordinary differential equations have been extended to evolution equations in Banach spaces. 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.

Table of Contents

Preface Acknowledgments 0 Introduction 1 Extending ordinary differential equations to metric spaces 2 Adapting mutational equations to examples in vector space 3 Continuity of distances replaces the triangle inequality 4 Introducing distribution-like solutions to mutational equations 5 Mutational inclusions in metric spaces Tools Bibliographical Notes References Index of Notation Index

Product Details

ISBN:
9783642124709
Author:
Lorenz, Thomas
Publisher:
Springer
Subject:
Mathematical Analysis
Subject:
Differential equations (ordinary
Subject:
Evolution equations
Subject:
Nonsmooth analysis
Subject:
Set-valued dynamics
Subject:
Well-posed initial value problems
Subject:
generalized)
Subject:
partial
Subject:
Analysis
Subject:
Dynamical Systems and Ergodic Theory
Subject:
ordinary differential equations
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Systems Theory, Control
Subject:
Mathematical and Computational Biology
Subject:
Mathematics-Analysis General
Copyright:
Edition Description:
2010
Series:
Lecture Notes in Mathematics
Series Volume:
1996
Publication Date:
20100608
Binding:
TRADE PAPER
Language:
English
Pages:
523
Dimensions:
235 x 155 mm 892 gr

Related Subjects

Computers and Internet » Networking » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Vector Analysis

Lecture Notes in Mathematics #1996: Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces New Trade Paper
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Product details 523 pages Not Avail - English 9783642124709 Reviews:
"Synopsis" by , Ordinary differential equations have been extended to evolution equations in Banach spaces. 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.
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