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

Springer, 2010. — 523 p.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.