| 期刊全稱 | A Stability Technique for Evolution Partial Differential Equations | | 期刊簡稱 | A Dynamical Systems | | 影響因子2023 | Victor A. Galaktionov,Juan Luis Vázquez | | 視頻video | http://file.papertrans.cn/143/142250/142250.mp4 | | 發(fā)行地址 | Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations.Written by established mathematicians at the forefront of their f | | 學科分類 | Progress in Nonlinear Differential Equations and Their Applications | | 圖書封面 |  | | 影響因子 | common 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 > 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 certai | | Pindex | Book 2004 |
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