Mutational Analysis : A Joint Framework for Cauchy Problems in and Beyond Vector Spaces / by Thomas Lorenz.

Format:

Book

Author/Creator:

Lorenz, Thomas, Dr., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1996.

Lecture Notes in Mathematics, 0075-8434 ; 1996

Language:

English

Subjects (All):

Global analysis (Mathematics).

Mathematics.

Differentiable dynamical systems.

Differential equations.

Differential equations, Partial.

System theory.

Analysis.

Real Functions.

Dynamical Systems and Ergodic Theory.

Ordinary Differential Equations.

Partial Differential Equations.

Systems Theory, Control.

Local Subjects:

Analysis.

Real Functions.

Dynamical Systems and Ergodic Theory.

Ordinary Differential Equations.

Partial Differential Equations.

Systems Theory, Control.

Physical Description:

1 online resource (XIV, 509 pages 57 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.

System Details:

text file PDF

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.

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.

Other Format:

Printed edition:

ISBN:

9783642124716

Access Restriction:

Restricted for use by site license.