Library of American University of Madaba
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Lorenz, Thomas.
Mutational Analysis A Joint Framework for Cauchy Problems in and Beyond Vector Spaces / [electronic resource] : by Thomas Lorenz. - XIV, 509p. online resource. - Lecture Notes in Mathematics, 1996 0075-8434 ; .
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.
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.
9783642124716
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.
QA299.6-433
515
Mutational Analysis A Joint Framework for Cauchy Problems in and Beyond Vector Spaces / [electronic resource] : by Thomas Lorenz. - XIV, 509p. online resource. - Lecture Notes in Mathematics, 1996 0075-8434 ; .
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.
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.
9783642124716
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.
QA299.6-433
515