Mutational Analysis

A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

von Thomas Lorenz

509 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783642124709
• Sprache: Englisch
• Erscheinungsdatum: 09.06.2010
• Genre: Mathematik/Analysis
• Verlag: Springer Berlin