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Wave propagation in a lattice KPP equation in random media

Author(s): Tzong-Yow Lee; Fred Torcaso
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 121-125.
MSC (1991): Primary 60J60; Secondary 35K55
Posted: November 4, 1997
Comment(s): Additional information about this paper
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Abstract | References | Similar articles | Additional information

Abstract: We extend a result of Freidlin and Gartner (1979) for KPP (Kolmogorov-Petrovskii-Piskunov) wave fronts to the case $d\ge 2$ for i.i.d. (independent and identically distributed) random media. We show a wave front propagation speed is attained for the discrete-space (lattice) KPP using a large deviation approach.


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Gartner, J. and Freidlin, M. I. (1979), On the propagation of concentration waves in periodic and random media, Dokl. Akad. Nauk SSSR 249, 521-525. (Russian) MR 81d:80005
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Sznitman, A. S. (1995), Crossing velocities and random lattice animals, Ann. Probab. 23, 1006-1023. MR 96j:60066
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Xin, Jack X. (1997), Analysis and modeling of front propagation in heterogeneous media, To appear in Surveys in Applied Math.
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Additional Information:

Tzong-Yow Lee
Affiliation: Department of Mathematics, University of Maryland, College Park, MD 20742
Email: tyl@math.umd.edu

Fred Torcaso
Affiliation: Department of Mathematics, University of Maryland, College Park, MD 20742
Email: torcaso@math.umd.edu

DOI: 10.1090/S1079-6762-97-00036-X
PII: S 1079-6762(97)00036-X
Keywords: KPP equation, random media, large deviations
Received by editor(s): June 20, 1997
Posted: November 4, 1997
Additional Notes: This work was supported under NSF Grant DMS-95-04177 while the second author was research assistant at the University of Maryland.
Communicated by: Mark Freidlin
Copyright of article: Copyright 1997, American Mathematical Society


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