Mutational analysis : a joint framework for Cauchy problems in and beyond vector spaces

書誌事項

Mutational analysis : a joint framework for Cauchy problems in and beyond vector spaces

Thomas Lorenz

(Lecture notes in mathematics, 1996)

Springer, c2010

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注記

Bibliography: p. 497-503

Includes index

内容説明・目次

内容説明

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.

目次

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.

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