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- W2088446671 abstract "In singular perturbation problems one frequently has a family (pi_eps)_{epsin]0,1]} of semiflows on a space X and a ‘singular limit flow’ pi_0 of this family which is defined only on a subspace X_0 of X. Moreover, pi_epsilon converges to pi_0 only in some ‘singular’ sense. Such a situation occurs, for example, in fast–slow systems of differential equations or in evolution equations on thin spatial domains.In this paper we prove a general singular Conley index continuation principle stating that every isolated invariant set K_0 of pi_0 can be continued to a nearby family K_epsilon of isolated invariant sets of pi_epsilon with the same Conley index. We illustrate this continuation result with damped wave equations on thin domains. This extends some results from our previous work." @default.
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- W2088446671 date "2002-06-01" @default.
- W2088446671 modified "2023-09-27" @default.
- W2088446671 title "On a general Conley index continuation principle for singular perturbation problems" @default.
- W2088446671 doi "https://doi.org/10.1017/s0143385702000378" @default.
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