{"product_id":"viability-invariance-and-applications","title":"Viability, Invariance and Applications","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.\u003cbr\u003e\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e- New concepts for multi-functions as the classical tangent vectors for functions \u003cbr\u003e- Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions \u003cbr\u003e- Clarifying examples, illustrations and numerous problems, completely and carefully solved\u003cbr\u003e- Illustrates the applications from theory into practice \u003cbr\u003e- Very clear and elegant style","brand":"Elsevier S \u0026 T","offers":[{"title":"perpetual","offer_id":45078489464929,"sku":"9780444527615","price":54.75,"currency_code":"KWD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0268\/9869\/4241\/files\/480_a9b649cc-4bc0-4ea9-a16d-a219ee19e8cf.jpg?v=1780614043","url":"https:\/\/ebooks.aafaqeducation.com\/products\/viability-invariance-and-applications","provider":"ebook.aafaqeducation","version":"1.0","type":"link"}