{"product_id":"9780817641467","title":"Progress in Nonlinear Differential Equations and Their Applications: A Dynamical Systems Approach","description":"\u003ch1\u003eProgress in Nonlinear Differential Equations and Their Applications: A Dynamical Systems Approach\u003c\/h1\u003e \u003ch2\u003eGalaktionov, Victor A.; Vázquez, Juan Luis\u003c\/h2\u003e \u003cp\u003ecommon feature is that these evolution problems can be formulated as asymptoti­ cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu­ tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ­ ential equation (NDE) (1) Ut = A(u) + C(u, t), t \u0026gt; 0, where u has values in a Banach space, like an LP space, A is an autonomous (time-independent) operator and C is an asymptotically small perturbation, so that C(u(t), t) ~ ° as t ~ 00 along orbits {u(t)} of the evolution in a sense to be made precise, which in practice can be quite weak. We work in a situation in which the autonomous (limit) differential equation (ADE) Ut = A(u) (2) has a well-known asymptotic behaviour, and we want to prove that for large times the orbits of the original evolution problem converge to a certain class of limits of the autonomous equation. More precisely, we want to prove that the orbits of (NDE) are attracted by a certain limit set [2* of (ADE), which may consist of equilibria of the autonomous equation, or it can be a more complicated object.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2003-12-12\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780817641467\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4612-2050-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 377\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":45378502525068,"sku":"9780817641467","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780817641467.jpg?v=1775703798","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780817641467","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}