Tensor Formats Based on Subspaces are Positively Invariant Sets for Laplacian-Like Dynamical Systems
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In this note, we show that the set of tensors with bounded rank are positively invariant sets for linear evolution equations defined by Laplacian-like operators. In consequence, once a trajectory of the system enters to this class of set, it will never leave it again.
KeywordsBanach Space Proper Orthogonal Decomposition Continuous Semigroup Tensor Format Tensor Representation
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- 2.A. Ammar, B. Mokdad, F. Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations. J. Non-Newtonian Fluid Mech. 144, 98–121 (2007)zbMATHGoogle Scholar
- 4.A. Falcó, W. Hackbusch, A. Nouy, Geometric structures in tensor representations, Preprint 9/2013 at Max Planck Institute for Mathematics in the Sciences, 2013Google Scholar
- 9.A. Lozinski, R.G. Owen, T.N. Phillips, The Langevin and the Fokker–Plank Equation in Polymer Rheology, Handbook of Numerical Analysis, ed. by P.G. Ciarlet. Numerical Methods for Non-Newtonian Fluids, vol. XVI (Elsevier, Amsterdam, 2011), pp. 211–303Google Scholar