WIAS Preprint No. 2881, (2021)

Gradient flows for bounded linear evolution equations


Authors

  • Renger, D. R. Michiel
    ORCID: 0000-0003-3557-3485
  • Schindler, Stefanie
    ORCID: 0000-0002-4005-7314

2020 Mathematics Subject Classification

  • 34G10 37L05 35P99

Keywords

  • Linear evolution equation, gradient system, gradient flow, spectral theory, geodesic lambda-convexity

DOI

10.20347/WIAS.PREPRINT.2881

Abstract

We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient flow, namely those for which the operator is real diagonalisable. The proof is constructive, from which we also derive geodesic lambda-convexity.

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