Geodesic
Well-posedness of semilinear heat equations in L 1
Laister, R.1 ; Sierżęga, M.2
1 Department of Engineering Design and Mathematics, University of the West of England, Bristol BS16 1QY, UK
2 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 709-725

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The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term f has only recently been resolved (Laister et al. (2016)). There, for the more difficult case of initial data in L1, a necessary and sufficient integral condition on f emerged. Here, subject to this integral condition, we consider other fundamental properties of solutions with L1 initial data of indefinite sign, namely: uniqueness, regularity, continuous dependence and comparison. We also establish sufficient conditions for the global-in-time continuation of solutions for small initial data in L1.

DOI : 10.1016/j.anihpc.2019.12.001
Keywords: Heat equation, Existence, Uniqueness, Continuous dependence, Comparison, Global solution

Laister, R. 1 ; Sierżęga, M. 2

1 Department of Engineering Design and Mathematics, University of the West of England, Bristol BS16 1QY, UK
2 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland 
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     title = {Well-posedness of semilinear heat equations in {\protect\emph{L}
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     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Laister, R.; Sierżęga, M. Well-posedness of semilinear heat equations in L
         1. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 709-725. doi: 10.1016/j.anihpc.2019.12.001

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