Viability, invariance and applications
C�arj�a, Ovidiu.
Viability, invariance and applications [electronic resource] / Ovidiu C�arj�a, Mihai Necula, Ioan I. Vrabie. - 1st ed. - Amsterdam ; Boston : Elsevier, 2007. - 1 online resource (xii, 344 p.) : ill. - North-Holland mathematics studies, 207 0304-0208 ; . - North-Holland mathematics studies ; 207. .
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.
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.
9780444527615 0444527613 9780080521664 (electronic bk.) 0080521665 (electronic bk.)
133439:133563 Elsevier Science & Technology http://www.sciencedirect.com
013683358 Uk
Differential equations.
Set theory.
Symmetry (Mathematics)
MATHEMATICS--Differential Equations--General.
Differential equations.
Set theory.
Symmetry (Mathematics)
Electronic books.
QA371 / .C37 2007
515.35
Viability, invariance and applications [electronic resource] / Ovidiu C�arj�a, Mihai Necula, Ioan I. Vrabie. - 1st ed. - Amsterdam ; Boston : Elsevier, 2007. - 1 online resource (xii, 344 p.) : ill. - North-Holland mathematics studies, 207 0304-0208 ; . - North-Holland mathematics studies ; 207. .
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.
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.
9780444527615 0444527613 9780080521664 (electronic bk.) 0080521665 (electronic bk.)
133439:133563 Elsevier Science & Technology http://www.sciencedirect.com
013683358 Uk
Differential equations.
Set theory.
Symmetry (Mathematics)
MATHEMATICS--Differential Equations--General.
Differential equations.
Set theory.
Symmetry (Mathematics)
Electronic books.
QA371 / .C37 2007
515.35