Abstract
In this paper, the first of a bipartite work, we consider an abstract, nonautonomous system of evolution equations of hyperbolic type, related to semilinear wave equations. Theorem 1 states that under certain assumptions the system admits a global center manifold, or equivalently a global decoupling function which is continuously differentiable with respect to its arguments, among which timet occurs. The difficult proof is presented in part II, i.e. the continuation of the present paper. For purposes of applications a local version of Theorem 1 is proved, i.e. the local center manifold Theorem 2. We obtain a series of applications both to abstract, nonautonomous wave equations and to concrete nonautonomous, semilinear wave equations subject to Neumann and Dirichlet boundary conditions.
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Scarpellini, B. Center manifolds of infinite dimensions I: Main results and applications. Z. angew. Math. Phys. 42, 1–32 (1991). https://doi.org/10.1007/BF00962056
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DOI: https://doi.org/10.1007/BF00962056