| 期刊全称 | A Stability Technique for Evolution Partial Differential Equations | | 期刊简称 | A Dynamical Systems | | 影响因子2023 | Victor A. Galaktionov,Juan Luis Vázquez | | 视频video | http://file.papertrans.cn/143/142250/142250.mp4 | | 发行地址 | 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 | | 学科分类 | Progress in Nonlinear Differential Equations and Their Applications | | 图书封面 |  | | 影响因子 | 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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