TY  - BOOK
AU  - C�arj�a,Ovidiu
AU  - Necula,Mihai
AU  - Vrabie,I.I.
TI  - Viability, invariance and applications
T2  - North-Holland mathematics studies,
SN  - 9780444527615
AV  - QA371 .C37 2007
U1  - 515.35 22
PY  - 2007///
CY  - Amsterdam, Boston
PB  - Elsevier
KW  - Differential equations
KW  - Set theory
KW  - Symmetry (Mathematics)
KW  - MATHEMATICS
KW  - Differential Equations
KW  - General
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references (p. 325-333) and indexes; 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 Carat�hodory 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. Carat�hodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation
N2  - 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
UR  - http://www.sciencedirect.com/science/book/9780444527615
UR  - http://www.sciencedirect.com/science/publication?issn=03040208&volume=207
ER  -