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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Spectral theory and self-similar blowup in wave equations
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by Roland Donninger;
Bull. Amer. Math. Soc. 61 (2024), 659-685
DOI: https://doi.org/10.1090/bull/1845
Published electronically: August 15, 2024

Abstract:

This is an expository article that describes the spectral-theoretic aspects in the study of the stability of self-similar blowup for nonlinear wave equations. The linearization near a self-similar solution leads to a genuinely nonself-adjoint operator which is difficult to analyze. The main goal of this article is to provide an accessible account of the only known method that is capable of providing sufficient spectral information to complete the stability analysis. The exposition is based on a mini course given at the Summer School on Geometric Dispersive PDEs in Obergurgl, Austria, in September 2022.
References
Bibliographic Information
  • Roland Donninger
  • Affiliation: Universität Wien, Fakultät für Mathematik Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
  • MR Author ID: 839104
  • ORCID: 0000-0002-4522-648X
  • Email: roland.donninger@univie.ac.at
  • Published electronically: August 15, 2024
  • Additional Notes: This work was supported by the Austrian Science Fund FWF, Project P 34560: “Stable blowup in supercritical wave equations”.
  • © Copyright 2024 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 61 (2024), 659-685
  • DOI: https://doi.org/10.1090/bull/1845
  • MathSciNet review: 4803604