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By Ovidiu Carja, Al. I. Cuza University 700506 Iasi, Romania Mihai Necula, Al. I. Cuza University 700506 Iasi, Romania Ioan I. Vrabie, Al. I. Cuza University 700506 Iasi, Romania
Description 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 Nagumo's 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.
Audience
Primary Markets:
Graduate students, specialists and researchers in O.D.E., P.D.E., Differential Inclusions, Optimal Control
Secondary Markets:
Physicists, Engineers, Chemists, Economists, Biologists.
Contents 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 Carath odory 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. Carath odory
perturbations of m-dissipative operators
Chapter 13. Applications
Solutions to the proposed problems
Bibliographical notes and comments
Bibliography
Name Index
Subject Index
Notation
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