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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
Entstehung:
Anmerkungen:
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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.