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On a generalized Boussinesq model around a rotating obstacle: Existence of strong solutions
Stability of positive constant steady states and their bifurcation in a biological depletion model
1. | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China, China |
References:
[1] |
H. L. Smith and P. Waltman, "The theory of the Chemostat: Dynamics of Microbial Competition," Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
[2] |
A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik, 12 (1972), 30-39.
doi: 10.1007/BF00289234. |
[3] |
T. Erneux and E. Reiss, Brusselator isolas, SIAM J. Appl. Math., 43 (1983), 1240-1246.
doi: 10.1137/0143082. |
[4] |
I. Lengyel and I. R. Epstein, Modeling of Turing structure in the Chlorite-iodide-malonic acid-starch reaction system, Science, 251 (1991), 650-652.
doi: 10.1126/science.251.4994.650. |
[5] |
J. Schnakenberg, Simple chemical reaction systems with limit cycle behavior, J. Theor. Biol., 81 (1979), 389-400.
doi: 10.1016/0022-5193(79)90042-0. |
[6] |
J. H. Wu, Global bifurcation of coexistence state for the competition model in the chemostat, Nonlinear Anal., 39 (2000), 817-835.
doi: 10.1016/S0362-546X(98)00250-8. |
[7] |
W. M. Ni and J. C. Wei, On positive solutions concentrating on spheres for the Gierer-Meinhardt system, J. Diff. Eqns., 221 (2006), 158-189.
doi: 10.1016/j.jde.2005.03.004. |
[8] |
R. Peng and M. X. Wang, Pattern formation in the Brusselator system, J. Math. Anal. Appl., 309 (2005), 151-166.
doi: 10.1016/j.jmaa.2004.12.026. |
[9] |
W. M. Ni and M. Tang, Turing patterns in the Lengyel-Epstein system for the CIMA reaction, Transactions of the American Mathematical Society, 357 (2005), 3953-3969.
doi: 10.1090/S0002-9947-05-04010-9. |
[10] |
J. Wei and M. Winter, Stationary multiple spots for reaction-diffusion systems, J. Math. Biol., 57 (2008), 53-89.
doi: 10.1007/s00285-007-0146-y. |
[11] |
J. H. Wu, Global solutions of a biological depletion model, J. Shaanxi Normal University (Nature Science Edition), 28 (2000), 26-29. |
[12] |
Y. Lou and W. M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Diff. Eqns., 131 (1996), 79-131.
doi: 10.1006/jdeq.1996.0157. |
[13] |
M. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Anal., 8 (1971), 321-340.
doi: 10.1016/0022-1236(71)90015-2. |
[14] |
P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Anal., 7 (1971), 487-513.
doi: 10.1016/0022-1236(71)90030-9. |
[15] |
W. M. Ni, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc., 45 (1998), 9-18. |
[16] |
I. Takagi, Point-condensation for a reaction-diffusion system, J. Diff. Eqns., 61 (1986), 208-249.
doi: 10.1016/0022-0396(86)90119-1. |
show all references
References:
[1] |
H. L. Smith and P. Waltman, "The theory of the Chemostat: Dynamics of Microbial Competition," Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
[2] |
A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik, 12 (1972), 30-39.
doi: 10.1007/BF00289234. |
[3] |
T. Erneux and E. Reiss, Brusselator isolas, SIAM J. Appl. Math., 43 (1983), 1240-1246.
doi: 10.1137/0143082. |
[4] |
I. Lengyel and I. R. Epstein, Modeling of Turing structure in the Chlorite-iodide-malonic acid-starch reaction system, Science, 251 (1991), 650-652.
doi: 10.1126/science.251.4994.650. |
[5] |
J. Schnakenberg, Simple chemical reaction systems with limit cycle behavior, J. Theor. Biol., 81 (1979), 389-400.
doi: 10.1016/0022-5193(79)90042-0. |
[6] |
J. H. Wu, Global bifurcation of coexistence state for the competition model in the chemostat, Nonlinear Anal., 39 (2000), 817-835.
doi: 10.1016/S0362-546X(98)00250-8. |
[7] |
W. M. Ni and J. C. Wei, On positive solutions concentrating on spheres for the Gierer-Meinhardt system, J. Diff. Eqns., 221 (2006), 158-189.
doi: 10.1016/j.jde.2005.03.004. |
[8] |
R. Peng and M. X. Wang, Pattern formation in the Brusselator system, J. Math. Anal. Appl., 309 (2005), 151-166.
doi: 10.1016/j.jmaa.2004.12.026. |
[9] |
W. M. Ni and M. Tang, Turing patterns in the Lengyel-Epstein system for the CIMA reaction, Transactions of the American Mathematical Society, 357 (2005), 3953-3969.
doi: 10.1090/S0002-9947-05-04010-9. |
[10] |
J. Wei and M. Winter, Stationary multiple spots for reaction-diffusion systems, J. Math. Biol., 57 (2008), 53-89.
doi: 10.1007/s00285-007-0146-y. |
[11] |
J. H. Wu, Global solutions of a biological depletion model, J. Shaanxi Normal University (Nature Science Edition), 28 (2000), 26-29. |
[12] |
Y. Lou and W. M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Diff. Eqns., 131 (1996), 79-131.
doi: 10.1006/jdeq.1996.0157. |
[13] |
M. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Anal., 8 (1971), 321-340.
doi: 10.1016/0022-1236(71)90015-2. |
[14] |
P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Anal., 7 (1971), 487-513.
doi: 10.1016/0022-1236(71)90030-9. |
[15] |
W. M. Ni, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc., 45 (1998), 9-18. |
[16] |
I. Takagi, Point-condensation for a reaction-diffusion system, J. Diff. Eqns., 61 (1986), 208-249.
doi: 10.1016/0022-0396(86)90119-1. |
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