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作者 Cârjă, Ovidiu
書名 Viability, invariance and applications [electronic resource] / Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie
出版項 Amsterdam ; Boston : Elsevier, 2007
國際標準書號 9780444527615
0444527613
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA371 .C37 2007    在架上    30340200485120
版本 1st ed
說明 xii, 344 p. : ill. ; 25 cm
系列 North-Holland mathematics studies, 0304-0208 ; 207
附註 Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007. Mode of access: World Wide Web. System requirements: Web browser. Title from title screen (viewed on July 25, 2007). Access may be restricted to users at subscribing institutions
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumos Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions as the classical tangent vectors for functions - Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved - Illustrates the applications from theory into practice - Very clear and elegant style
Preface -- Chapter 1. Generalities -- Chapter 2. Specific preliminary results -- Ordinary differential equations and inclusions -- Chapter 3. Nagumo type viability theorems -- Chapter 4. Problems of invariance -- Chapter 5. Viability under Caraťhodory conditions -- Chapter 6. Viability for differential inclusions -- Chapter 7. Applications -- Part 2 Evolution equations and inclusions -- Chapter 8. Viability for single-valued semilinear evolutions -- Chapter 9. Viability for multi-valued semilinear evolutions -- Chapter 10. Viability for single-valued fully nonlinear evolutions -- Chapter 11. Viability for multi-valued fully nonlinear evolutions -- Chapter 12. Caraťhodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation
Includes bibliographical references (p. 325-333) and indexes
鏈接 Original 9780444527615 0444527613 (OCoLC)85690133
主題 Differential equations
Set theory
Symmetry (Mathematics)
Electronic books. local
Alt Author Necula, Mihai
Vrabie, I. I. (Ioan I.), 1951-
ScienceDirect (Online service)
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