Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line |
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Authors: | Nguyen Thieu Huy |
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Institution: | Faculty of Applied Mathematics and Informatics, Hanoi University of Technology, Khoa Toan-Tin ung dung, DH Bach Khoa Hanoi, 1 Dai Co Viet, Hanoi, Viet Nam |
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Abstract: | Consider an evolution family U=(U(t,s))t?s?0 on a half-line R+ and an integral equation . 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. |
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Keywords: | Evolution equations Integral equations Exponential stability of solutions Exponential dichotomy Admissibility of function spaces Perturbations |
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