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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Viability, Invariance and Applications, Volume 207 (Hardcover, 207th edition)
Loot Price: R3,289
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Viability, Invariance and Applications, Volume 207 (Hardcover, 207th edition)
Series: North-Holland Mathematics Studies
Expected to ship within 12 - 17 working days
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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.
- 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
General
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