| Author(s) |
Du, Yihong
Matsuzawa, Hiroshi
Zhou, Maolin
|
| Publication Date |
2014
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| 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
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| ISSN |
1095-7154
0036-1410
|
| Link | |
| Language |
en
|
| Publisher |
Society for Industrial and Applied Mathematics
|
| Title |
Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems
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| Type of document |
Journal Article
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| Entity Type |
Publication
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