L-shadowing lemma for the Cauchy equation

2024/06/06 by Lee, K., Morales, C. A.
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 54G99 #Secondary 37B05

paper · doi:10.48550/arxiv.2406.03951

Abstract

We prove that if the Cauchy problem u=Au in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach \citeo, o1 for linear homeomorphisms. Some short applications are given.

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