Introduction to the Theory of Differential Inclusions is popular PDF and ePub book, written by Georgi V. Smirnov in 2022-02-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Introduction to the Theory of Differential Inclusions can be Read Online from any device for your convenience.
Introduction to the Theory of Differential Inclusions Book PDF Summary
A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.
Detail Book of Introduction to the Theory of Differential Inclusions PDF
- Author : Georgi V. Smirnov
- Release : 22 February 2022
- Publisher : American Mathematical Society
- ISBN : 9781470468545
- Genre : Mathematics
- Total Page : 226 pages
- Language : English
- PDF File Size : 7,8 Mb
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