Well-posedness of semilinear heat equations in L1

  • R. Laister

    Department of Engineering Design and Mathematics, University of the West of England, Bristol BS16 1QY, UK
  • M. Sierżęga

    Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Well-posedness of semilinear heat equations in L1 cover

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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 , a necessary and sufficient integral condition on f emerged. Here, subject to this integral condition, we consider other fundamental properties of solutions with 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 .

Cite this article

R. Laister, M. Sierżęga, Well-posedness of semilinear heat equations in L1. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 3, pp. 709–725

DOI 10.1016/J.ANIHPC.2019.12.001