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.
Included in series
North-Holland Mathematics Studies
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.
