• Medientyp: E-Artikel
  • Titel: Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity
  • Beteiligte: Agresti, Antonio [Verfasser:in]; Veraar, Mark [Verfasser:in]
  • Erschienen: Elsevier, 2023
  • Erschienen in: Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations . 2023;368(9):247-300. doi: 10.1016/j.jde.2023.05.038
  • Sprache: Englisch
  • DOI: https://doi.org/10.1016/j.jde.2023.05.038
  • ISSN: 0022-0396; 1090-2732
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  • Beschreibung: In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.
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