SHARP ESTIMATE OF THE SPREADING SPEED DETERMINED BY NONLINEAR FREE BOUNDARY PROBLEMS.
In: SIAM Journal on Mathematical Analysis, Jg. 46 (2014), Heft 1, S. 375-396
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Zugriff:
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. [ABSTRACT FROM AUTHOR]
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SHARP ESTIMATE OF THE SPREADING SPEED DETERMINED BY NONLINEAR FREE BOUNDARY PROBLEMS.
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Autor/in / Beteiligte Person: | YIHONG, DU ; HIROSHI, MATSUZAWA ; MAOLIN, ZHOU |
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Zeitschrift: | SIAM Journal on Mathematical Analysis, Jg. 46 (2014), Heft 1, S. 375-396 |
Veröffentlichung: | 2014 |
Medientyp: | academicJournal |
ISSN: | 0036-1410 (print) |
DOI: | 10.1137/130908063 |
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