Well-posedness of semilinear heat equations in L1

Laister, Robert; Sier??ga, M.

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