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

• Main Author: Lorenz, Thomas. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Mathematics, 1996
• Subjects: Mathematics.; Global analysis (Mathematics).; Differentiable dynamical systems.; Differential Equations.; Differential equations, partial.; Biology > Mathematics.; Systems theory.; Analysis.; Dynamical Systems and Ergodic Theory.; Ordinary Differential Equations.; Partial Differential Equations.; Systems Theory, Control.; Mathematical Biology in General.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-12471-6

 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.