A geometric construction of traveling waves in a bioremediation model

Journal of Nonlinear Science

Volumn 16, Issue 4, 2006, Pages 329-349

  Beck, M ^a   Doelman, A ^b   Kaper, T J ^a  

^a Boston University   (United States)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867926677     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-005-0731-4     Document Type: Article

References (13)

1. J. G. Blom and P. A. Zegeling. Algorithm 731: A moving grid interface for systems of one-dimensional time-dependent partial differential equations. ACM Transactions on Mathematical Software, 20(2):194-214, 1994.
2. N. Fenichel. Persistence and smoothness of invariant manifolds for flows. Ind. Univ. Math. J., 21:193-226, 1971.
3. N. Fenichel. Geometric singular perturbation theory for ordinary differential equations. J. Diff. Eq., 31(1):53-98, 1979.
4. C. K. R. T. Jones. Geometric singular perturbation theory. In R. Johnson, editor, Dynamical Systems, volume 1609 of Lecture Notes in Mathematics, pages 44-118. Springer-Verlag, Berlin, 1994.
5. H. Keijzer, R. J. Schotting, and S.E.A.T.M. van der Zee. Semi-analytical traveling wave solution of one-dimensional aquifer bioremediation. Commun. Appl. Numer. Anal., 7(1):1-20, 2000.
6. R. Murray and J. X. Xin. Existence of traveling waves in a biodegradation model for organic contaminants. SIAM J. Math. Anal., 30(1):72-94, 1998. (Pubitemid 128767657)
7. J. E. Odencrantz. Modeling the biodegradation kinetics of dissolved organic contaminants in a heterogeneous two-dimensional aquifer. PhD thesis, University of Illinois, Urbana, 1992.
8. J. E. Odencrantz, A. J. Valocchi, and B. E. Rittmann. Modeling the interaction of sorption and biodegradation on transport in ground water in situ bioremediation systems. In E. Poeter, S. Ashlock, and J. Proud, editors, Proceedings of the 1993 Groundwater Modeling Conference, pages 2-3 to 2-12, Golden, CO, 1993. Int. Ground Water Model. Cent.
9. S. Oya and A. J. Valocchi. Characterization of traveling waves and analytical estimation of pollutant removal in one-dimensional subsurface bioremediation modeling.Water Resources Research, 33(5):1117-1127, 1997.
10. S. Oya and A. J. Valocchi. Analytical approximation of biodegradation rate for in situ bioremediation of groundwater under ideal radial flow conditions. J. Contaminant Hydrology, 31:65-83, 1998.
11. P. Szmolyan. Transversal heteroclinic and homoclinic orbits in singular perturbation problems. J. Diff. Eq., 92:252-281, 1991.
12. A. J.Valocchi, J. E. Odencrantz, and B. E. Rittmann. Computational studies of the transport of reactive solutes: Interaction between adsorption and biotransformation. In S. Y.Wang, editor, Proceedings of the First International Conference on Hydro-Science and Engineering, vol. 1, pages 1845-1852, Washington, D.C., 1993.
13. J. X. Xin and J. M. Hyman. Stability, relaxation, and oscillation of biodegradation fronts. SIAM J. Appl. Math., 61(2):472-505, 2000.