Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains

Laister, Robert; Robinson, James C.; Sierzega, Mikolaj

Abstract

We establish a local non-existence result for the equation ut-δu=f(u) with Dirichlet boundary conditions on a smooth bounded domain Ω⊂Rn and initial data in Lq(Ω) when the source term f is non-decreasing and limsups→∞s-γf(s)=∞ for some exponent γ>q(1+2/n). This allows us to construct a locally Lipschitz f satisfying the Osgood condition ∫1∞1/f(s)ds=∞, which ensures global existence for initial data in L∞(Ω), such that for every q with 1≤q

• Journal Article Type: Article
• Publication Date: Jan 1, 2014
• Publicly Available Date: Jun 6, 2019
• Journal: Comptes Rendus Mathematique
• Print ISSN: 1631-073X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 352
• Issue: 7-8
• Pages: 621-626
• DOI: https://doi.org/10.1016/j.crma.2014.05.010
• Keywords: local solutions, semilinear heat equations, Osgood, bounded domains
• Public URL: https://uwe-repository.worktribe.com/output/825225
• Publisher URL: http://dx.doi.org/10.1016/j.crma.2014.05.010