TY  - BOOK
AU  - Lorenz,Thomas
ED  - SpringerLink (Online service)
TI  - Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces 
T2  - Lecture Notes in Mathematics,
SN  - 9783642124716
AV  - QA299.6-433 
U1  - 515 23
PY  - 2010///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Differentiable dynamical systems
KW  - Differential Equations
KW  - Differential equations, partial
KW  - Biology
KW  - Systems theory
KW  - Analysis
KW  - Dynamical Systems and Ergodic Theory
KW  - Ordinary Differential Equations
KW  - Partial Differential Equations
KW  - Systems Theory, Control
KW  - Mathematical Biology in General
N1  - 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
N2  - 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-12471-6
ER  -