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https://hdl.handle.net/1959.11/18244
Title: | Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems | Contributor(s): | Du, Yihong (author) ; Matsuzawa, Hiroshi (author); Zhou, Maolin (author) | Publication Date: | 2014 | DOI: | 10.1137/130908063 | Handle Link: | https://hdl.handle.net/1959.11/18244 | Abstract: | We study nonlinear diffusion problems of the form ut = uxx + f(u) with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundaries representing the expanding fronts. For monostable, bistable, and combustion types of nonlinearities, Du and Lou ["Spreading and vanishing in nonlinear diffusion problems with free boundaries," J. Eur. Math. Soc. (JEMS), to appear] obtained a rather complete description of the long-time dynamical behavior of the problem and revealed sharp transition phenomena between spreading (limt→∞u(t, x) = 1) and vanishing (limt→∞ u(t, x) = 0). They also determined the asymptotic spreading speed of the fronts by making use of semiwaves when spreading happens. In this paper, we give a much sharper estimate for the spreading speed of the fronts than that in the above-mentioned work of Du and Lou, and we describe how the solution approaches the semiwave when spreading happens. | Publication Type: | Journal Article | Grant Details: | ARC/DP120100727 | Source of Publication: | SIAM Journal on Mathematical Analysis, 46(1), p. 375-396 | Publisher: | Society for Industrial and Applied Mathematics | Place of Publication: | United States of America | ISSN: | 1095-7154 0036-1410 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations | Fields of Research (FoR) 2020: | 490410 Partial differential equations | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article |
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