Du, Yihong; Matsuzawa, Hiroshi; Zhou, Maolin

Author(s)

Du, Yihong

Matsuzawa, Hiroshi

Zhou, Maolin

Publication Date

2014

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.

Citation

SIAM Journal on Mathematical Analysis, 46(1), p. 375-396

ISSN

1095-7154

0036-1410

Link

https://hdl.handle.net/1959.11/18244

Publisher

Society for Industrial and Applied Mathematics

Title

Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems

Type of document

Journal Article

Entity Type

Publication

Author(s)	Du, Yihong Matsuzawa, Hiroshi Zhou, Maolin
Publication Date	2014
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.
Citation	SIAM Journal on Mathematical Analysis, 46(1), p. 375-396
ISSN	1095-7154 0036-1410
Link	https://hdl.handle.net/1959.11/18244
Publisher	Society for Industrial and Applied Mathematics
Title	Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems
Type of document	Journal Article
Entity Type	Publication

Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems

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