Solutions with snaking singularities for the fast diffusion equation

Fila, Marek; King, John Robert; Takahashi, Jin; Yanagida, Eiji

Abstract

We construct solutions of the fast diffusion equation, which exist for all t ∈ R and are singular on the set γ(t) := is(s);-∞ < s ≤ ct, c > 0, where ∈ C3(R;Rn), n ≥ 2. We also give a precise description of the behavior of the solutions near γ (t).

Citation

Fila, M., King, J. R., Takahashi, J., & Yanagida, E. (2021). Solutions with snaking singularities for the fast diffusion equation. Transactions of the American Mathematical Society, 374(12), 8775-8792. https://doi.org/10.1090/tran/8479

• Journal Article Type: Article
• Acceptance Date: May 5, 2021
• Online Publication Date: Sep 15, 2021
• Publication Date: 2021
• Deposit Date: Aug 16, 2021
• Publicly Available Date: Sep 15, 2021
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 374
• Issue: 12
• Pages: 8775-8792
• DOI: https://doi.org/10.1090/tran/8479
• Keywords: Applied Mathematics; General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/6053780
• Publisher URL: https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2021-08479-2/home.html#Additional
• Additional Information: First published in Transactions of the American Mathematical Society, [63 (April 2016)], published by the American Mathematical Society. © 2021 American Mathematical Society.