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 semilinear heat equations with Dirichlet boundary conditions and initial data in L^q when the source term f is non-decreasing. We construct a locally Lipschitz f satisfying the Osgood condition (which ensures global existence for bounded initial data), such that for every q there is an initial condition in L^q for which the corresponding semilinear problem has no local-in-time solution.

Citation

Laister, R., Robinson, J. C., & Sierzega, M. (2014). Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains. Comptes Rendus Mathématique, 352(7-8), 621-626. https://doi.org/10.1016/j.crma.2014.05.010

• Journal Article Type: Article
• Publication Date: Jan 1, 2014
• 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