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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):
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Abstract:
We extend a result of Freidlin and Gartner (1979) for KPP (Kolmogorov-Petrovskii-Piskunov) wave fronts to the case 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.
References:
- 1.
- Dembo, A. and Zeitouni, O. (1993), Large deviation techniques and applications, Jones and Bartlett Publishers, Boston, MA. MR 95a:60034
- 2.
- Freidlin, M. I. (1985), Functional integration and partial differential equations, Annals of Mathematical Studies, vol. 109, Princeton University Press. MR 87g:60066
- 3.
- 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
- 4.
- Liggett, Thomas (1985), Interacting particle systems, Springer-Verlag. MR 86e:60089
- 5.
- Sznitman, A. S. (1994), Shape theorem, Lyapounov exponents, and large deviations for Brownian motion in a Poissonian potential, Comm. Pure Appl. Math. 47, 1655-1688. MR 96b:60217
- 6.
- Sznitman, A. S. (1995), Crossing velocities and random lattice animals, Ann. Probab. 23, 1006-1023. MR 96j:60066
- 7.
- Xin, Jack X. (1997), Analysis and modeling of front propagation in heterogeneous media, To appear in Surveys in Applied Math.
- 8.
- Zerner, Martin (1997), Directional decay of the Green's function for a random nonnegative potential on
, To appear in Annals of Applied Probability.
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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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