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Well-posedness of semilinear heat equations in L1

Laister, Robert; Sier??ga, M.

Well-posedness of semilinear heat equations in L1 Thumbnail


Authors

M. Sier??ga



Abstract

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 .

Journal Article Type Article
Acceptance Date Dec 4, 2019
Online Publication Date Dec 30, 2019
Publication Date May 1, 2020
Deposit Date Dec 11, 2019
Publicly Available Date Dec 31, 2020
Journal Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Print ISSN 0294-1449
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 37
Issue 3
Pages 709-725
DOI https://doi.org/10.1016/j.anihpc.2019.12.001
Keywords heat equation; existence; uniqueness; continuous dependence; comparison; global solution
Public URL https://uwe-repository.worktribe.com/output/4773656

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