Well-posedness of semilinear heat equations in <i>L</i>
         <sup>1</sup>

Laister, R.; Sierżęga, M.

doi:10.1016/j.anihpc.2019.12.001

Geodesic

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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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Résumé

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 $L^{1}$ , a necessary and sufficient integral condition on f emerged. Here, subject to this integral condition, we consider other fundamental properties of solutions with $L^{1}$ 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 $L^{1}$ .

Zbl

DOI : 10.1016/j.anihpc.2019.12.001

Keywords: Heat equation, Existence, Uniqueness, Continuous dependence, Comparison, Global solution

Affiliations des auteurs :

Laister, R. ¹ ; Sierżęga, M. ²

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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. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.12.001/

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