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Limiting behaviour of invariant manifolds for a system of singularly perturbed evolution equations
Author(s) -
Ševčovič Daniel
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170805
Subject(s) - mathematics , singular perturbation , limiting , invariant manifold , invariant (physics) , mathematical analysis , manifold (fluid mechanics) , slow manifold , perturbation (astronomy) , mathematical physics , physics , mechanical engineering , quantum mechanics , engineering
In this paper we consider a class of specific singularly perturbed abstract evolution equations. It is shown that, for small values of the singular parameter, the invariant manifold for the perturbed equation is C 1 close to that of the unpertubed equation. The results obtained are applied to the second‐order evolution equations with strong damping arising in the mathematical théory of viscoelasticity.