Mutational Analysis A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

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.