Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces
1. Auflage. 2010
ISBN: 978-3-642-12470-9
Verlag: Springer

Buch, Englisch, Band 1996, 509 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 894 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Lorenz, Thomas

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.