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- W2017622445 abstract "Let Ω ⊂ R N be a smooth bounded domain. Let be a second-order strongly elliptic differential operator with smooth symmetric coefficients. Let B denote the Dirichlet or the Neumann boundary operator. We prove the existence of a smooth potential a : Ω → R such that all sufficiently small vector fields on R N + 1 can be realized on the centre manifold of the semilinear parabolic equation by an appropriate nonlinearity f : ( x , s , w ) ∈ Ω x R x R N ↦ f ( x , s , w ) ∈ R. For N = 2, n , k ∈ N , we prove the existence of a smooth potential a : Ω → R such that all sufficiently small k -jets of vector fields on R n can be realized on the centre manifold of the semilinear parabolic equation by an appropriate nonlinearity f : ( x , s ) ∈ Ω x R ↦ f ( x , s ) ∈ R 2 ( here, ‘·’ denotes the scalar product in R 2 )." @default.
- W2017622445 created "2016-06-24" @default.
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- W2017622445 date "2000-04-01" @default.
- W2017622445 modified "2023-09-27" @default.
- W2017622445 title "Perturbation of elliptic operators and complex dynamics of parabolic partial differential equations" @default.
- W2017622445 doi "https://doi.org/10.1017/s0308210500000226" @default.
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