The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
Front Propagation in Heterogeneous Media
Abstract
A review is presented of recent results on front propagation in reaction-diffusion-advection equations in homogeneous and heterogeneous media. Formal asymptotic expansions and heuristic ideas are used to motivate the results wherever possible. The fronts include constant-speed monotone traveling fronts in homogeneous media, periodically varying traveling fronts in periodic media, and fluctuating and fractal fronts in random media. These fronts arise in a wide range of applications such as chemical kinetics, combustion, biology, transport in porous media, and industrial deposition processes. Open problems are briefly discussed along the way.
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Cites
Partial Differential Equations
(1988) · Lecture Notes in Mathematics · doi:10.1007/bfb0082920 · Cited by 23,383
Elliptic Partial Differential Equations of Second Order
Gilbarg, D., & Trudinger, N. S. (2001) · Classics in Mathematics · doi:10.1007/978-3-642-61798-0 · Cited by 18,587
Perturbation Theory for Linear Operators
Kato, T. (1995) · Classics in Mathematics · doi:10.1007/978-3-642-66282-9 · Cited by 16,290
Convergence of Probability Measures
Billingsley, P. (1999) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316962 · Cited by 13,910
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Dynamic Scaling of Growing Interfaces
Kardar, M., Parisi, G., & Zhang, Y.-C. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.889 · Cited by 5,380
THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES
FISHER, R. A. (1937) · Annals of Eugenics · doi:10.1111/j.1469-1809.1937.tb02153.x · Cited by 4,883
User’s guide to viscosity solutions of second order partial differential equations
Crandall, M. G., Ishii, H., & Lions, P.-L. (1992) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1992-00266-5 · Cited by 4,781
Asymptotic Analysis for Periodic Structures
Bensoussan, A., Lions, J. L., & Papanicolaou, G. (2011) · American Mathematical Society eBooks · doi:10.1090/chel/374 · Cited by 4,523
Fractal Concepts in Surface Growth
Barabási, A. L., & Stanley, H. E. (1995) · doi:10.1017/cbo9780511599798 · Cited by 3,925
Cited by
(2002) · Handbook of Dynamical Systems · doi:10.1016/s1874-575x(02)80039-x · Cited by 405
Metadata
- Authors
- Xin, J.
- Venue
- SIAM Review
- Published
- 2000-01
- Volume
- 42
- Issue
- 2
- Pages
- 161-230
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2015242641
- Cited by
- 542
- References
- 39
- FWCI
- 29.46
- Type
- journal article
- Language
- en
- Open access
- closed
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