Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30771
Title: Asymptotic properties of a free boundary problem for a reaction-di usion equation with multi-stable nonlinearity
Authors: Yamada, Yoshio
Keywords: free boundary problemreaction-diffusion equationasymptotic profilespreading
Issue Date: 2020
Publisher: EUT Edizioni Università di Trieste
Source: Yoshio Yamada, "Asymptotic properties of a free boundary problem for a reaction-di usion equation with multi-stable nonlinearity" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
This paper deals with a free boundary problem for a reaction-diffusion equation with moving boundary, whose dynamics is governed by the Stefan condition. We will mainly discuss the problem for the case of multi-stable nonlinearity, which is a function with a multiple number of positive stable equilibria. The first result is concerned with the classi cation of solutions in accordance with large-time behaviors. As a consequence, one can observe a multiple number of spreading phenomena corresponding for each positive stable equilibrium. Here it is seen that there exists a certain group of spreading solutions whose element accompanies a propagating terrace. We will derive sharp asymptotic estimates of free boundary and profile of every spreading solution including spreading one with propagating terrace.
Type: Article
URI: http://hdl.handle.net/10077/30771
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30771
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), in progress

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