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- W648896631 abstract "Suppose Σ is an n-dimensional integral surface in Y, that is, an n-dimensional manifold without boundary that is positively invariant. Let, for each u ∈Σ P(u) denote the projector on the tangent space T u (Σ) to Σ at u. Let us assume that the surface is blocked in the sense that $$lambda left( {Pleft( u right)} right) > frac{{{lambda _n} + {lambda _{n + 1}}}}{2}{text{ for all }}u$$ (7.1) and that λ n = Λ m which satisfies condition (3.13). Let us consider u o ∈ H and assume that the distance between uo and Σ is attained at some u1 ∈ Σ Then, clearly P(u1)(u1 − u1)= 0. Let us consider the trajectories S(t)uo, S(t)u1. Their difference w(t) = S(t)uo − S(t)u1 satisfies (4.1). Denoting Λ(t) = (Aw(t), w(t))|w(t)|2, we have as in Chapter 4: $$frac{d}{{dt}}|wleft( t right){|^2}left( {{k_4}Lambda left( t right) - {k_7}} right)|w{|^2} leqslant 0.$$ (7.2)" @default.
- W648896631 created "2016-06-24" @default.
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- W648896631 date "1989-01-01" @default.
- W648896631 modified "2023-10-08" @default.
- W648896631 title "Local Exponential Decay Toward Blocked Integral Surfaces" @default.
- W648896631 doi "https://doi.org/10.1007/978-1-4612-3506-4_8" @default.
- W648896631 hasPublicationYear "1989" @default.
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