Abstract
Under mild conditions it is proved that an invariant submanifold ofX α0⩽β<1 for the equationdx/dt+Ax=f(x), A sectorial,f∈C'(X α,X),0⩽α<1, is a submanifold ofX 1 as well. In addition, conditions are given for the semiflow of the equation to extend fromX α toX and a new inertial manifold theorem is proved for the scalar reaction diffusion equation.
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Brunovský, P., Tereščák, I. Regularity of invariant manifolds. J Dyn Diff Equat 3, 313–337 (1991). https://doi.org/10.1007/BF01049735
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DOI: https://doi.org/10.1007/BF01049735