Invariant manifolds of partial functional differential equations |
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Authors: | Nguyen Van Minh Jianhong Wu |
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Institution: | a Department of Mathematics, Hanoi University of Science, Khoa Toan, DH Khoa Hoc Tu Nhien, 334 Nguyen Trai, Hanoi, Viet Nam b Department of Mathematics and Statistics, York University, Toronto, Ont., Canada M3J 1P3 |
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Abstract: | This paper is concerned with the existence, smoothness and attractivity of invariant manifolds for evolutionary processes on general Banach spaces when the nonlinear perturbation has a small global Lipschitz constant and locally Ck-smooth near the trivial solution. Such a nonlinear perturbation arises in many applications through the usual cut-off procedure, but the requirement in the existing literature that the nonlinear perturbation is globally Ck-smooth and has a globally small Lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut-off function. Our general results are illustrated by and applied to partial functional differential equations for which the phase space (where r>0 and being a Banach space) has no smooth inner product structure and for which the validity of variation-of-constants formula is still an interesting open problem. |
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Keywords: | primary 34K19 37L10 secondary 35B40 34G20 |
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