-
Previous Article
Well-posedness for a model of individual clustering
- DCDS-B Home
- This Issue
-
Next Article
Pattern formation of the attraction-repulsion Keller-Segel system
Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation
1. | College of Liberal Arts and Sciences, Tokyo Medical and Dental University, 2-8-30 Kohnodai, Ichikawa, Chiba 272-0827, Japan |
2. | Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan |
References:
[1] |
J. London Math. Soc. (2), 74 (2006), 453-474.
doi: 10.1112/S0024610706023015. |
[2] |
Math. Biosci., 56 (1981), 217-237.
doi: 10.1016/0025-5564(81)90055-9. |
[3] |
With the collaboration of Michel Artola, Michel Cessenat and Hélène Lanchon. Translated from the French by Alan Craig. Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[4] |
C. R. Acad. Sci. Paris, 310 (1990), 559-562. |
[5] |
Research in Applied Mathematics, vol. 37, John-Wiley and Sons, Chichester, 1994. |
[6] |
Ann. Scoula Norm. Sup. Pisa Cl. Sci. IV, 24 (1997), 633-683. |
[7] |
J. Math. Biol., 58 (2009), 183-217.
doi: 10.1007/s00285-008-0201-3. |
[8] |
Jahresber. Deutsch. Math.-Verein., 105 (2003), 103-165. |
[9] |
Jahresber. Deutsch. Math.-Verein., 106 (2004), 51-69. |
[10] |
European J. Appl. Math., 12 (2001), 159-177.
doi: 10.1017/S0956792501004363. |
[11] |
Trans. Amer. Math. Soc., 329 (1992), 819-824.
doi: 10.1090/S0002-9947-1992-1046835-6. |
[12] |
J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[13] |
GAKUTO Internat. Ser. Math. Sci. Appl., 29 (2008), 265-278. |
[14] |
Physica D, 241 (2012), 1629-1639.
doi: 10.1016/j.physd.2012.06.009. |
[15] |
Physica A, 230 (1996), 499-543.
doi: 10.1016/0378-4371(96)00051-9. |
[16] |
Springer-Verlag, New York, 2003. |
[17] |
Nonlinear Anal., 74 (2011), 286-297.
doi: 10.1016/j.na.2010.08.044. |
[18] |
Adv. Math. Sci. Appl., 5 (1995), 581-601. |
[19] |
J. Inequal. Appl., 6 (2001), 37-55.
doi: 10.1155/S1025583401000042. |
[20] |
Nonlinear Anal., 51 (2002), 119-144.
doi: 10.1016/S0362-546X(01)00815-X. |
[21] |
Funkcial. Ekvac., 44 (2001), 441-469. |
[22] |
Adv. Math. Sci. Appl., 12 (2002), 587-606. |
[23] |
Physica D: Nonlinear Phenomena, 240 (2011), 363-375.
doi: 10.1016/j.physd.2010.09.011. |
[24] |
Progress in Nonlinear Differential Equations and their Applications, 62. Birkhäuser Boston, Inc., Boston, MA, 2005.
doi: 10.1007/0-8176-4436-9. |
[25] |
Comm. Partial Differential Equations, 32 (2007), 849-877.
doi: 10.1080/03605300701319003. |
[26] |
Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1997. |
[27] |
Bull. Math. Biol., 70 (2008), 1570-1607.
doi: 10.1007/s11538-008-9322-5. |
[28] |
Johann Ambrosius Barth Verlag, Heidelberg/Leipzig, 1995. |
[29] |
J. Math. Anal. Appl., 348 (2008), 708-729.
doi: 10.1016/j.jmaa.2008.07.071. |
[30] |
Comm. Partial Differential Equations, 35 (2010), 1516-1537.
doi: 10.1080/03605300903473426. |
[31] |
J. Differential Equations, 248 (2010), 2889-2905.
doi: 10.1016/j.jde.2010.02.008. |
[32] |
Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04631-5. |
show all references
References:
[1] |
J. London Math. Soc. (2), 74 (2006), 453-474.
doi: 10.1112/S0024610706023015. |
[2] |
Math. Biosci., 56 (1981), 217-237.
doi: 10.1016/0025-5564(81)90055-9. |
[3] |
With the collaboration of Michel Artola, Michel Cessenat and Hélène Lanchon. Translated from the French by Alan Craig. Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[4] |
C. R. Acad. Sci. Paris, 310 (1990), 559-562. |
[5] |
Research in Applied Mathematics, vol. 37, John-Wiley and Sons, Chichester, 1994. |
[6] |
Ann. Scoula Norm. Sup. Pisa Cl. Sci. IV, 24 (1997), 633-683. |
[7] |
J. Math. Biol., 58 (2009), 183-217.
doi: 10.1007/s00285-008-0201-3. |
[8] |
Jahresber. Deutsch. Math.-Verein., 105 (2003), 103-165. |
[9] |
Jahresber. Deutsch. Math.-Verein., 106 (2004), 51-69. |
[10] |
European J. Appl. Math., 12 (2001), 159-177.
doi: 10.1017/S0956792501004363. |
[11] |
Trans. Amer. Math. Soc., 329 (1992), 819-824.
doi: 10.1090/S0002-9947-1992-1046835-6. |
[12] |
J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[13] |
GAKUTO Internat. Ser. Math. Sci. Appl., 29 (2008), 265-278. |
[14] |
Physica D, 241 (2012), 1629-1639.
doi: 10.1016/j.physd.2012.06.009. |
[15] |
Physica A, 230 (1996), 499-543.
doi: 10.1016/0378-4371(96)00051-9. |
[16] |
Springer-Verlag, New York, 2003. |
[17] |
Nonlinear Anal., 74 (2011), 286-297.
doi: 10.1016/j.na.2010.08.044. |
[18] |
Adv. Math. Sci. Appl., 5 (1995), 581-601. |
[19] |
J. Inequal. Appl., 6 (2001), 37-55.
doi: 10.1155/S1025583401000042. |
[20] |
Nonlinear Anal., 51 (2002), 119-144.
doi: 10.1016/S0362-546X(01)00815-X. |
[21] |
Funkcial. Ekvac., 44 (2001), 441-469. |
[22] |
Adv. Math. Sci. Appl., 12 (2002), 587-606. |
[23] |
Physica D: Nonlinear Phenomena, 240 (2011), 363-375.
doi: 10.1016/j.physd.2010.09.011. |
[24] |
Progress in Nonlinear Differential Equations and their Applications, 62. Birkhäuser Boston, Inc., Boston, MA, 2005.
doi: 10.1007/0-8176-4436-9. |
[25] |
Comm. Partial Differential Equations, 32 (2007), 849-877.
doi: 10.1080/03605300701319003. |
[26] |
Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1997. |
[27] |
Bull. Math. Biol., 70 (2008), 1570-1607.
doi: 10.1007/s11538-008-9322-5. |
[28] |
Johann Ambrosius Barth Verlag, Heidelberg/Leipzig, 1995. |
[29] |
J. Math. Anal. Appl., 348 (2008), 708-729.
doi: 10.1016/j.jmaa.2008.07.071. |
[30] |
Comm. Partial Differential Equations, 35 (2010), 1516-1537.
doi: 10.1080/03605300903473426. |
[31] |
J. Differential Equations, 248 (2010), 2889-2905.
doi: 10.1016/j.jde.2010.02.008. |
[32] |
Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04631-5. |
[1] |
Ying Yang. Global classical solutions to two-dimensional chemotaxis-shallow water system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2625-2643. doi: 10.3934/dcdsb.2020198 |
[2] |
Harumi Hattori, Aesha Lagha. Global existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021071 |
[3] |
Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021066 |
[4] |
Masashi Wakaiki, Hideki Sano. Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021021 |
[5] |
Brahim Alouini. Finite dimensional global attractor for a class of two-coupled nonlinear fractional Schrödinger equations. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021013 |
[6] |
Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237 |
[7] |
Xuemin Deng, Yuelong Xiao, Aibin Zang. Global well-posedness of the $ n $-dimensional hyper-dissipative Boussinesq system without thermal diffusivity. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1229-1240. doi: 10.3934/cpaa.2021018 |
[8] |
Wided Kechiche. Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021031 |
[9] |
Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393 |
[10] |
Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228 |
[11] |
Simão Correia, Mário Figueira. A generalized complex Ginzburg-Landau equation: Global existence and stability results. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021056 |
[12] |
Hong Yi, Chunlai Mu, Guangyu Xu, Pan Dai. A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2537-2559. doi: 10.3934/dcdsb.2020194 |
[13] |
Xu Pan, Liangchen Wang. Boundedness and asymptotic stability in a quasilinear two-species chemotaxis system with nonlinear signal production. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021064 |
[14] |
Nouressadat Touafek, Durhasan Turgut Tollu, Youssouf Akrour. On a general homogeneous three-dimensional system of difference equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2021017 |
[15] |
Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 |
[16] |
Irena PawŃow, Wojciech M. Zajączkowski. Global regular solutions to three-dimensional thermo-visco-elasticity with nonlinear temperature-dependent specific heat. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1331-1372. doi: 10.3934/cpaa.2017065 |
[17] |
Lu Xu, Chunlai Mu, Qiao Xin. Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3031-3043. doi: 10.3934/dcds.2020396 |
[18] |
Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001 |
[19] |
Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021091 |
[20] |
Miroslav Bulíček, Victoria Patel, Endre Süli, Yasemin Şengül. Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021053 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]