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On a chemotaxis model with saturated chemotactic flux
1. | Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States |
2. | Mathematics Department, Tulane University, New Orleans, LA 70118 |
3. | Department of Mathematics, Capital Normal University, Beijing 100048, China |
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Ann. Scuola Normale Superiore Pisa Cl. Sci. (4), 24 (1997), 633-683. |
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J. Sci. Comput., 39 (2009), 115-128.
doi: 10.1007/s10915-008-9252-2. |
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Discrete Contin. Dyn. Syst. Ser. B, 7 (2007), 125-144 (electronic).
doi: 10.3934/dcdsb.2007.7.125. |
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J. Math. Biol., 58 (2009), 183-217.
doi: 10.1007/s00285-008-0201-3. |
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Jahresber. DMV, 105 (2003), 103-165. |
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Jahresber. DMV, 106 (2004), 51-69. |
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J. Differential Equations, 215 (2005), 52-107.
doi: 10.1016/j.jde.2004.10.022. |
[22] |
J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[23] |
J. Theor. Biol., 30 (1971), 225-234.
doi: 10.1016/0022-5193(71)90050-6. |
[24] |
Translated from the Russian by S. Smith, Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., 1967. |
[25] |
World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
[26] |
J. Differential Equations, 72 (1988), 1-27.
doi: 10.1016/0022-0396(88)90147-7. |
[27] |
Funkcial. Ekvac., 40 (1997), 411-433. |
[28] |
Notices Amer. Math. Soc., 45 (1998), 9-18. |
[29] |
J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
[30] |
Bull. Math. Biophys., 15 (1953), 311-338.
doi: 10.1007/BF02476407. |
[31] |
Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. |
[32] |
J. Anal. Math., 76 (1998), 289-319.
doi: 10.1007/BF02786939. |
[33] |
Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. |
[34] |
3rd ed., Wm. C. Brown Publishers, Chicago-London, 1996. Google Scholar |
[35] |
Chem. Eng. Sci., 44 (1989), 1-17.
doi: 10.1016/0009-2509(89)85098-5. |
[36] |
J. Differential Equations, 246 (2009), 2788-2812.
doi: 10.1016/j.jde.2008.09.009. |
[37] |
SIAM J. Appl. Math., 65 (2005), 790-817 (electronic).
doi: 10.1137/S0036139902415117. |
[38] |
SIAM J. Math. Anal., 31 (2000), 535-560 (electronic).
doi: 10.1137/S0036141098339897. |
[39] |
Biophys. J., 68 (1995), 2181-2189.
doi: 10.1016/S0006-3495(95)80400-5. |
show all references
References:
[1] |
Ann. Rev. Biochem., 44 (1975), 341-356.
doi: 10.1146/annurev.bi.44.070175.002013. |
[2] |
J. Math. Biol., 9 (1980), 147-177.
doi: 10.1007/BF00275919. |
[3] |
Differential Integral Equations, 3 (1990), 13-75. |
[4] |
in "Function Spaces, Differential Operators and Nonlinear Analysis" (Friedrichroda, 1992), Teubner-Texte Math., 133, Teubner, Stuttgart, (1993), 9-126. |
[5] |
2nd ed., Princeton University Press, Princeton, New Jersey, 1967. Google Scholar |
[6] |
Nature, 349 (1991), 630-633.
doi: 10.1038/349630a0. |
[7] |
Nature, 376 (1995), 49-53.
doi: 10.1038/376049a0. |
[8] |
A. Chertock, Y. Epshteyn and A. Kurganov, High-order finite-difference and finite-volume methods for chemotaxis models,, in preparartion., (). Google Scholar |
[9] |
Math. Biosc., 56 (1981), 217-237.
doi: 10.1016/0025-5564(81)90055-9. |
[10] |
J. Theor. Biol., 31 (1971), 101-118.
doi: 10.1016/0022-5193(71)90124-X. |
[11] |
J. Functional Analysis, 8 (1971), 321-340.
doi: 10.1016/0022-1236(71)90015-2. |
[12] |
Arch. Rational Mech. Anal., 52 (1973), 161-180.
doi: 10.1007/BF00282325. |
[13] |
SIAM Rev., 43 (2001), 89-112.
doi: 10.1137/S003614450036757X. |
[14] |
Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[15] |
Ann. Scuola Normale Superiore Pisa Cl. Sci. (4), 24 (1997), 633-683. |
[16] |
J. Sci. Comput., 39 (2009), 115-128.
doi: 10.1007/s10915-008-9252-2. |
[17] |
Discrete Contin. Dyn. Syst. Ser. B, 7 (2007), 125-144 (electronic).
doi: 10.3934/dcdsb.2007.7.125. |
[18] |
J. Math. Biol., 58 (2009), 183-217.
doi: 10.1007/s00285-008-0201-3. |
[19] |
Jahresber. DMV, 105 (2003), 103-165. |
[20] |
Jahresber. DMV, 106 (2004), 51-69. |
[21] |
J. Differential Equations, 215 (2005), 52-107.
doi: 10.1016/j.jde.2004.10.022. |
[22] |
J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[23] |
J. Theor. Biol., 30 (1971), 225-234.
doi: 10.1016/0022-5193(71)90050-6. |
[24] |
Translated from the Russian by S. Smith, Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., 1967. |
[25] |
World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
[26] |
J. Differential Equations, 72 (1988), 1-27.
doi: 10.1016/0022-0396(88)90147-7. |
[27] |
Funkcial. Ekvac., 40 (1997), 411-433. |
[28] |
Notices Amer. Math. Soc., 45 (1998), 9-18. |
[29] |
J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
[30] |
Bull. Math. Biophys., 15 (1953), 311-338.
doi: 10.1007/BF02476407. |
[31] |
Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. |
[32] |
J. Anal. Math., 76 (1998), 289-319.
doi: 10.1007/BF02786939. |
[33] |
Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. |
[34] |
3rd ed., Wm. C. Brown Publishers, Chicago-London, 1996. Google Scholar |
[35] |
Chem. Eng. Sci., 44 (1989), 1-17.
doi: 10.1016/0009-2509(89)85098-5. |
[36] |
J. Differential Equations, 246 (2009), 2788-2812.
doi: 10.1016/j.jde.2008.09.009. |
[37] |
SIAM J. Appl. Math., 65 (2005), 790-817 (electronic).
doi: 10.1137/S0036139902415117. |
[38] |
SIAM J. Math. Anal., 31 (2000), 535-560 (electronic).
doi: 10.1137/S0036141098339897. |
[39] |
Biophys. J., 68 (1995), 2181-2189.
doi: 10.1016/S0006-3495(95)80400-5. |
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