Existence and Non-Existence of Fisher-KPP Transition Fronts
Publication
, Journal Article
Nolen, J; Roquejoffre, JM; Ryzhik, L; Zlatoš, A
Published in: Archive for Rational Mechanics and Analysis
2012
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global-in-time solutions while creating a global-in-time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized inhomogeneity leads to the existence of transition fronts, but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media. © 2011 Springer-Verlag.
Duke Scholars
Published In
Archive for Rational Mechanics and Analysis
DOI
ISSN
0003-9527
Publication Date
2012
Volume
203
Issue
1
Start / End Page
217 / 246
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
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APA
Chicago
ICMJE
MLA
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Nolen, J., Roquejoffre, J. M., Ryzhik, L., & Zlatoš, A. (2012). Existence and Non-Existence of Fisher-KPP Transition Fronts. Archive for Rational Mechanics and Analysis, 203(1), 217–246. https://doi.org/10.1007/s00205-011-0449-4
Nolen, J., J. M. Roquejoffre, L. Ryzhik, and A. Zlatoš. “Existence and Non-Existence of Fisher-KPP Transition Fronts.” Archive for Rational Mechanics and Analysis 203, no. 1 (2012): 217–46. https://doi.org/10.1007/s00205-011-0449-4.
Nolen J, Roquejoffre JM, Ryzhik L, Zlatoš A. Existence and Non-Existence of Fisher-KPP Transition Fronts. Archive for Rational Mechanics and Analysis. 2012;203(1):217–46.
Nolen, J., et al. “Existence and Non-Existence of Fisher-KPP Transition Fronts.” Archive for Rational Mechanics and Analysis, vol. 203, no. 1, 2012, pp. 217–46. Scival, doi:10.1007/s00205-011-0449-4.
Nolen J, Roquejoffre JM, Ryzhik L, Zlatoš A. Existence and Non-Existence of Fisher-KPP Transition Fronts. Archive for Rational Mechanics and Analysis. 2012;203(1):217–246.
Published In
Archive for Rational Mechanics and Analysis
DOI
ISSN
0003-9527
Publication Date
2012
Volume
203
Issue
1
Start / End Page
217 / 246
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics