Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line

By N. Huy. 2006

123 citations recorded by the source corpus.

Consider an evolution family U = (U (t, s))ts0 on a half-line R+ and an integral equation u(t) = U(t,s)u(s) + � t s U( t,ξ) f (ξ )dξ . We characterize the exponential dichotomy of the evolution family through solvability of this integral equation in admissible function spaces which contain wide classes of function spaces like function spaces of Lp type, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory. We then apply our results to study the robustness of the exponential dichotomy of evolution families on a half-line under small perturbations.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b346c308291698c88a6a3250bf66e918c92f004a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

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

In Control and Systems Engineering

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

Citations in the corpus

• 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]).”