Mutational Analysis A Joint Framework for Cauchy Problems in and Beyond Vector Spaces - Lorenz, Thomas; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2010)
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.
Extending Ordinary Differential Equations to Metric Spaces: Aubin$1 (Bs 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.s
Keywords: Mathematics; Global analysis (Mathematics).; Differentiable dynamical systems; Differential Equations; Differential equations, partial; Biology -- Mathematics; Systems theory; Mathematics; Analysis; Dynamical Systems and Ergodic Theory; Ordinary Differential Equations; Partial Differential Equations; Systems Theory, Control; Mathematical Biology in General