Dichotomies for evolution equations in Banach spaces
Codruta Stoica (IMB)
TL;DR
This paper explores various dichotomy concepts for evolution equations in Banach spaces, highlighting their significance in analyzing stable, unstable, and central manifolds through the asymptotic behavior of solutions.
Contribution
It systematically reviews and emphasizes different dichotomy notions in Banach space evolution equations, linking them to the stability analysis of manifolds.
Findings
Different types of dichotomies are characterized for evolution equations.
Asymptotic behaviors of solutions are linked to stability properties.
The role of skew-evolution semiflows in studying asymptotics is highlighted.
Abstract
The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banach spaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the solutions of the evolution equations are studied by means of the asymptotic behaviors for skew-evolution semiflows.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis · advanced mathematical theories