Stability of Traveling Waves of a Solute Transport Equation

Journal of Differential Equations

Volumn 135, Issue 2, 1997, Pages 269-298

  Xin, Jack X ^a  

^a The University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000462819     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.3228     Document Type: Article

References (28)

1. Aiki T., Shinoda J., Kenmochi N. Periodic stability for some degenerate parabolic equations with nonlinear flux boundary conditions. Nonlinear Anal. TMA. 17:1991;885-902.
2. Aronson D. G. The Porous Medium Equation. Lecture Notes in Math. No. 1224:1985.
3. Berestycki H., Nirenberg L. Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. Analysis etc. 1990;Academic Press, New York.
4. Berestycki H., Nirenberg L. On the method of moving planes and the sliding method. Bol. Soc. Brasil Mat. 22:1991;1-37.
5. Bolt G. H. Soil Chemistry B, Physical-Chemical Models. Developments in Soil Science 5B. 1979.
6. Bosma W. J. P., van der Zee S. E . A. T. M. Transport of reacting solute in a one-dimensional chemically heterogeneous porous media. Water Resources Res. 29:1993;117-131.
7. Crandall M. G., Tartar L. Some relations between non-expensive and order preserving mappings. Proc. Amer. Math. Soc. 78:1980;385-390.
8. DiBenedetto E. Degenerate Parabolic Equations. 1993;Springer-Verlag, Berlin/New York.
9. Dunford N., Schwartz J. T. Linear Operators, Part I, General Theory. 1958;Interscience, New York.
10. van Duijn C. J., Knabner P. Travelling waves in the transport of reactive solutes through porous media, adsorption and binary ion exchange: Part I and II. Transport in Porous Media. 8:1992.
11. van Duijn C. J., Knabner P. Solute transport in porous media with equilibrium and nonequilibrium multiple sites adsorption, travelling waves. J. Reine Angew. Math. 415:1991;1-49.
12. Gohberg I. C., Krein M. G. Introduction to the theory of linear non-selfadjoint operators. Trans. Amer. Math. Soc. 18:1969.
13. Grundy R. E., van Duijn C. J., Dawson C. N. Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media: The fast reaction case. Q. J. Mech. Appl. Math. 47:1994;69-106.
14. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. Vol. 840:1981;Springer-Verlag, Berlin/New York.
15. Il'in A. M., Oleinik O. A. Behavior of the solutions of the Cauchy problem for certain quasilinear equations for unbounded increase of time. AMS Transl. Ser. 2. 42:1964;19-23.
16. Ladyzhenskaja O. A., Solonikov V. A. Linear and Quasi-Linear Equations of Parabolic Type. 1968;AMS, Providence.
17. Kato T. Perturbation Theory for Linear Operators. 1966;Springer-Verlag, Berlin/New York.
18. Lax P. D. Regional Conf. Ser. in Appl. Math. No. 11:1973.
19. 1. Comm. Pure Appl. Math. 35:1982;737-749.
20. M. Postel, J. Xin, 1996, Numerical study of fronts in random media using a reactive solute transport model, Univ. Heidelberg.
21. Sattinger D. H. On the stability of waves of nonlinear parabolic systems. Adv. Math. 22:1976;312-355.
22. Smoller J. Shock Waves and Reaction-Diffusion Equations. 1983;Springer-Verlag, Berlin/New York.
23. Vol'pert A. I., Hudjaev S. I. Cauchy's problem for degenerate second order quasilinear parabolic equations. Math. USSR Sb. 1969;365-387.
24. Wehr J., Xin J. White noise perturbation of the viscous shock fronts of the Burgers equation. Comm. Math. Phys. 181:1996;183-203.
25. Xin X. Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity. J. Dynamics Differential Equations. 3:1991;541-573.
26. Xin J. X. Existence of Multidimensional Traveling Waves in Transport of Reactive Solutes through Periodic Porous Media. Arch. Rational Mech. Anal. 128:1994;75-103.
27. van der Zee S. E. A. T. M., van Riemsdijk W. H. Transport of reactive solute in spatially variable soil systems. Water Resources Res. 23:1987;2059-2069.
28. Nonlinear Anal. TMA. 19:1992;1111-1120.