Characterizations of Dichotomies of Evolution Equations on the Half-Line

By Nguyen Van Minh, N. Huy. 2001

62 citations recorded by the source corpus.

Abstract In this paper we investigate the characterization of dichotomies of an evolution family U  = (U(t, s))t ≥ s ≥ 0 of bounded linear operators on Banach space X. We introduce operators I0 and IX on subspaces of Lp(R+ , X) using the integral equation u(t) = U(t, s)u(s) + ∫ts U(t, ξ)f(ξ)dξ. The exponential and ordinary dichotomies of U are characterized by properties of I0, IX.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/fcea70427a3390fb4822838ea5d10944daf2f655

How researchers see this paper

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In Applied Mathematics

1. Luís Barreira
2. Cláudia Valls
3. N. Huy
4. César M. Silva
5. A. J. G. Bento
6. Daniel Thompson

In Control and Systems Engineering

1. Cláudia Valls
2. Luís Barreira
3. N. Huy
4. Adam Czornik
5. Michal Niezabitowski
6. César M. Silva
7. A. J. G. Bento

In Modeling and Simulation

1. N. Huy

Citations in the corpus

• Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line (2006, methodology): “2,5]), for bounded A(t) in Banach spaces (see [6,15]) and for concrete function spaces (see [16,17] and references therein).”
• Robustness of nonuniform exponential dichotomies in Banach spaces (2008, background): “For details and references we refer to the book of Chicone and Latushkin [8] (see in particular the final remarks of Chapters 3 and 4), and for more recent work to Huy [16] (we mention in particular the papers [21,22,28]).”