-
Previous Article
Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source
- DCDS-S Home
- This Issue
-
Next Article
Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
On a Parabolic-ODE system of chemotaxis
1. | Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain |
2. | Departamento de Matemática Aplicada, E.T.S.I. Sistemas Informáticos, Universidad Politécnica de Madrid 28031, Spain |
3. | Center for Computation and Simulation, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain |
$u$ |
$v$ |
$ \mathbb{R}^n$ |
$v$ |
$v_t = h(u, v).$ |
$ h_v+χ u h_u>0 $ |
$g$ |
$h_v+χ u h_u = 0$ |
$g \equiv 0$ |
References:
[1] |
A. R. A. Anderson and M. A. I. Chaplain,
Continuous and discrete mathematical models of
tumor-induced angiogenesis, Bull. Math. Biology, 60 (1998), 857-899.
doi: 10.1006/bulm.1998.0042. |
[2] |
T. Black,
Global existence and asymptotic stability in a competitive two-species chemotaxis
system with two signals, Discrete& Continuous Dynamical Systems-Series B, 22 (2017), 1253-1272.
doi: 10.3934/dcdsb.2017061. |
[3] |
T. Black, J. Lankeit and M. Mizukami,
On the weakly competitive case in a two-species
chemotaxis model, IMA J Appl Math., 81 (2016), 860-876.
doi: 10.1093/imamat/hxw036. |
[4] |
T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán and F. Jülicher, Morphogen
transport in Epithelia, Physical Review E Stat Nonlin Soft Matter Phys, 75 (2007), 011901.
doi: 10.1103/PhysRevE.75.011901. |
[5] |
N. Bellomo, A. Bellouquid, Y. Tao and M. Winkler,
Toward a mathematical theory of
Keller-Segel models of pattern formation in biological tissues, Mathematical Models and Methods in Applied Sciences, 25 (2015), 1663-1763.
doi: 10.1142/S021820251550044X. |
[6] |
C. Conca and E. Espejo,
Threshold condition for global existence and blow-up to a radially
symmetric drift-diffusion system, Appl. Math. Lett., 25 (2012), 352-356.
doi: 10.1016/j.aml.2011.09.013. |
[7] |
L. Edelstein-Keshet,
Mathematical Models in Biology, Society for Industrial and Applied Mathematics, Philadelphia 2005.
doi: 10.1137/1.9780898719147. |
[8] |
A. Fasano, A. Mancini and M. Primicerio,
Equilibrium of two populations subject to chemotaxis, Math. Models Methods Appl. Sci., 14 (2004), 503-533.
doi: 10.1142/S0218202504003337. |
[9] |
M. A. Fontelos, A. Friedman and B. Hu,
Mathematical analysis of a model for the initiation
of angiogenesis, SIAM Math. Anal., 33 (2002), 1330-1355.
doi: 10.1137/S0036141001385046. |
[10] |
A. Friedman and J. I. Tello,
Stability of solutions of chemotaxis equations in reinforced random walks, J. Math. Anal. Appl., 272 (2002), 138-163.
doi: 10.1016/S0022-247X(02)00147-6. |
[11] |
M. Hirata, S. Kurima, M. Mizukami and T. Yokota,
Boundedness and stabilization in a twodimensional two-species chemotaxis-Navier- Stokes system with competitive kinetics, Journal of Differential Equations, 263 (2017), 470-490.
doi: 10.1016/j.jde.2017.02.045. |
[12] |
D. Horstmann,
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Jahresber. Dtsch. Math. Ver., 105 (2003), 103-165.
|
[13] |
D. Horstmann,
Generalizing the Keller-Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and
repulsion between competitive interacting species, J. Nonlinear Sci., 21 (2011), 231-270.
doi: 10.1007/s00332-010-9082-x. |
[14] |
E. F. Keller and L. A. Segel,
Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[15] |
E. F. Keller and L. A. Segel,
A model for chemotaxis, J. Theoret. Biol., 30 (1971), 225-234.
doi: 10.1016/0022-5193(71)90050-6. |
[16] |
H. Kielhöfer,
Bifurcation Theory, Springer, 2004.
doi: 10.1007/b97365. |
[17] |
P. Krzyżanowski, P. Laurençot and D. Wrzosek,
Mathematical models of receptor-mediated transport of morphogens, M3AS, 20 (2010), 2021-2052.
doi: 10.1142/S0218202510004866. |
[18] |
A. Kubo, H. Hoshino and K. Kimura,
Global existence and asymptotic behaviour of solutions
for nonlinear evolution equations related to a tumour invasion, Proceedings of 10th AIMS Conference, (2015), 733-744.
doi: 10.3934/proc.2015.0733. |
[19] |
A. Kubo and T. Suzuki,
Mathematical models of tumour angiogenesis, Journal of Computational and Applied Mathematics, 204 (2007), 48-55.
doi: 10.1016/j.cam.2006.04.027. |
[20] |
A. Kubo and J. I. Tello,
Mathematical analysis of a model of chemotaxis with competition
terms, Differential and Integral Equations, 29 (2016), 441-454.
|
[21] |
D. A. Lauffenburger,
Quantitative studies of bacterial chemotaxis and microbial population
dynamics, Microb. Ecol., 22 (1991), 175-185.
doi: 10.1007/BF02540222. |
[22] |
H. A. Levine and B. D. Sleeman,
A system of reaction diffusion equation arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57 (1997), 683-730.
doi: 10.1137/S0036139995291106. |
[23] |
H. A. Levine and J. Renclawowicz,
Singularity formation in chemotaxis - a conjecture of
nagai, SIAM J. Appl. Math., 65 (2004), 336-360.
doi: 10.1137/S0036139903431725. |
[24] |
H. A. Levine, B. P. Sleeman and N. Nilsen-Hamilton,
A mathematical modeling for the roles
of pericytes and macrophages in the initiation of angiogenesis I. The role of protease inhibitors
in preventing angiogenesis, Mathematical Biosciences, 168 (2000), 75-115.
doi: 10.1016/S0025-5564(00)00034-1. |
[25] |
Y. Li, K. Lin and C. Mu,
Boundedness and asymptotic behavior of solutions to a chemotaxishaptotaxis model in high dimensions, Applied Mathematics Letters, 50 (2015), 91-97.
doi: 10.1016/j.aml.2015.06.010. |
[26] |
M. Malogrosz,
Well-posedness and asymptotic behavior of a multidimensonal model of morphogen transport, J. Evol. Eq., 12 (2012), 353-366.
doi: 10.1007/s00028-012-0135-5. |
[27] |
M. Małogrosz,
A model of morphogen transport in the presence of glypicans II, Journal of Mathematical Analysis and Applications, 433 (2016), 642-680.
doi: 10.1016/j.jmaa.2015.07.053. |
[28] |
J. H. Merking, D. J. Needham and B. D. Sleeman,
A mathematical model for the spread of
morphogens with density dependent chemosensitivity, Nonlinearity, 18 (2005), 2745-2773.
doi: 10.1088/0951-7715/18/6/018. |
[29] |
J. H. Merking and B. D. Sleeman,
On the spread of morphogens, J. Math. Biol., 51 (2005), 1-17.
doi: 10.1007/s00285-004-0308-0. |
[30] |
M. Mizukami and T. Yokota,
Global existence and asymptotic stability of solutions to a twospecies chemotaxis system with any chemical diffusion, J. Differential Equations, 261 (2016), 2650-2669.
doi: 10.1016/j.jde.2016.05.008. |
[31] |
A.I. Muñoz and J. I. Tello,
Mathematical analysis and numerical simulation of a model of morphogenesis, Mathematical Biosciences and Engineering, 8 (2011), 1035-1059.
doi: 10.3934/mbe.2011.8.1035. |
[32] |
M. Negreanu and J. I. Tello,
On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., 46 (2014), 3761-3781.
doi: 10.1137/140971853. |
[33] |
M. Negreanu and J. I. Tello,
On a comparison method to reaction-diffusion systems and its
applications to chemotaxis, Discrete and Continuous Dynamical Systems-Series B, 18 (2013), 2669-2688.
doi: 10.3934/dcdsb.2013.18.2669. |
[34] |
M. Negreanu and J. I. Tello,
On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., 46 (2014), 3761-3781.
doi: 10.1137/140971853. |
[35] |
M. Negreanu and J. I. Tello,
Asymptotic stability of a two species chemotaxis system with
non-diffusive chemoattractant, J. Differential Equations, 258 (2015), 1592-1617.
doi: 10.1016/j.jde.2014.11.009. |
[36] |
C. S. Patlak,
Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, 15 (1953), 311-338.
doi: 10.1007/BF02476407. |
[37] |
H. G. Othmer and A. Stevens,
Aggregation, blowup, and collapse: The ABC$^{\prime}$s of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), 1044-1081.
|
[38] |
B. D. Sleeman and H. A. Levine,
Partial differential equations of chemotaxis and angiogenesis, Math. Methods Appl. Sci., 24 (2001), 405-426.
doi: 10.1002/mma.212. |
[39] |
B. D. Sleeman and H. A. Levine,
Partial differential equations of chemotaxis and angiogenesis, SIAM J. Appl. Math., 65 (2005), 790-817.
doi: 10.1137/S0036139902415117. |
[40] |
A. Stevens,
The derivation of chemotaxis equations as limit dynamics of moderately interacting stochactic many-particle systems, SIAM J. Appl. Math., 61 (2000), 183-212.
doi: 10.1137/S0036139998342065. |
[41] |
C. Stinner, J. I. Tello and M. Winkler,
Mathematical analysis of a model of chemotaxis arising from morphogenesis, Math. Methods Appl. Sci., 35 (2012), 445-465.
doi: 10.1002/mma.1573. |
[42] |
C. Stinner, J. I. Tello and M. Winkler,
Competitive exclusion in a two-species chemotaxis
model, Journal of Mathematical Biology, 68 (2014), 1607-1626.
doi: 10.1007/s00285-013-0681-7. |
[43] |
T. Suzuki,
Mathematical models of tumor growth systems, Mathematica Bohemica, 137 (2012), 201-218.
|
[44] |
T. Suzuki and R. Takahashi,
Global in time solution to a class of tumour growth systems, Adv. Math. Sci. Appl., 19 (2009), 503-524.
|
[45] |
J. I. Tello,
Mathematical analysis of a model of Morphogenesis, Discrete and Continuous Dynamical Systems - Serie A., 25 (2009), 343-361.
doi: 10.3934/dcds.2009.25.343. |
[46] |
J. I. Tello and M. Winkler,
Stabilization in a two-species chemotaxis system with a logistic
source, Nonlinearity, 25 (2012), 1413-1425.
doi: 10.1088/0951-7715/25/5/1413. |
[47] |
A. M. Turing,
The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society of London, Series B, 237 (1952), 37-72.
doi: 10.1098/rstb.1952.0012. |
[48] |
X. Wang and Y. Wu,
Qualitative analysis on a chemotactic diffusion model for two species
competing for a limited resource, Quart. Appl. Math., 60 (2002), 505-531.
doi: 10.1090/qam/1914439. |
show all references
References:
[1] |
A. R. A. Anderson and M. A. I. Chaplain,
Continuous and discrete mathematical models of
tumor-induced angiogenesis, Bull. Math. Biology, 60 (1998), 857-899.
doi: 10.1006/bulm.1998.0042. |
[2] |
T. Black,
Global existence and asymptotic stability in a competitive two-species chemotaxis
system with two signals, Discrete& Continuous Dynamical Systems-Series B, 22 (2017), 1253-1272.
doi: 10.3934/dcdsb.2017061. |
[3] |
T. Black, J. Lankeit and M. Mizukami,
On the weakly competitive case in a two-species
chemotaxis model, IMA J Appl Math., 81 (2016), 860-876.
doi: 10.1093/imamat/hxw036. |
[4] |
T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán and F. Jülicher, Morphogen
transport in Epithelia, Physical Review E Stat Nonlin Soft Matter Phys, 75 (2007), 011901.
doi: 10.1103/PhysRevE.75.011901. |
[5] |
N. Bellomo, A. Bellouquid, Y. Tao and M. Winkler,
Toward a mathematical theory of
Keller-Segel models of pattern formation in biological tissues, Mathematical Models and Methods in Applied Sciences, 25 (2015), 1663-1763.
doi: 10.1142/S021820251550044X. |
[6] |
C. Conca and E. Espejo,
Threshold condition for global existence and blow-up to a radially
symmetric drift-diffusion system, Appl. Math. Lett., 25 (2012), 352-356.
doi: 10.1016/j.aml.2011.09.013. |
[7] |
L. Edelstein-Keshet,
Mathematical Models in Biology, Society for Industrial and Applied Mathematics, Philadelphia 2005.
doi: 10.1137/1.9780898719147. |
[8] |
A. Fasano, A. Mancini and M. Primicerio,
Equilibrium of two populations subject to chemotaxis, Math. Models Methods Appl. Sci., 14 (2004), 503-533.
doi: 10.1142/S0218202504003337. |
[9] |
M. A. Fontelos, A. Friedman and B. Hu,
Mathematical analysis of a model for the initiation
of angiogenesis, SIAM Math. Anal., 33 (2002), 1330-1355.
doi: 10.1137/S0036141001385046. |
[10] |
A. Friedman and J. I. Tello,
Stability of solutions of chemotaxis equations in reinforced random walks, J. Math. Anal. Appl., 272 (2002), 138-163.
doi: 10.1016/S0022-247X(02)00147-6. |
[11] |
M. Hirata, S. Kurima, M. Mizukami and T. Yokota,
Boundedness and stabilization in a twodimensional two-species chemotaxis-Navier- Stokes system with competitive kinetics, Journal of Differential Equations, 263 (2017), 470-490.
doi: 10.1016/j.jde.2017.02.045. |
[12] |
D. Horstmann,
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Jahresber. Dtsch. Math. Ver., 105 (2003), 103-165.
|
[13] |
D. Horstmann,
Generalizing the Keller-Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and
repulsion between competitive interacting species, J. Nonlinear Sci., 21 (2011), 231-270.
doi: 10.1007/s00332-010-9082-x. |
[14] |
E. F. Keller and L. A. Segel,
Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[15] |
E. F. Keller and L. A. Segel,
A model for chemotaxis, J. Theoret. Biol., 30 (1971), 225-234.
doi: 10.1016/0022-5193(71)90050-6. |
[16] |
H. Kielhöfer,
Bifurcation Theory, Springer, 2004.
doi: 10.1007/b97365. |
[17] |
P. Krzyżanowski, P. Laurençot and D. Wrzosek,
Mathematical models of receptor-mediated transport of morphogens, M3AS, 20 (2010), 2021-2052.
doi: 10.1142/S0218202510004866. |
[18] |
A. Kubo, H. Hoshino and K. Kimura,
Global existence and asymptotic behaviour of solutions
for nonlinear evolution equations related to a tumour invasion, Proceedings of 10th AIMS Conference, (2015), 733-744.
doi: 10.3934/proc.2015.0733. |
[19] |
A. Kubo and T. Suzuki,
Mathematical models of tumour angiogenesis, Journal of Computational and Applied Mathematics, 204 (2007), 48-55.
doi: 10.1016/j.cam.2006.04.027. |
[20] |
A. Kubo and J. I. Tello,
Mathematical analysis of a model of chemotaxis with competition
terms, Differential and Integral Equations, 29 (2016), 441-454.
|
[21] |
D. A. Lauffenburger,
Quantitative studies of bacterial chemotaxis and microbial population
dynamics, Microb. Ecol., 22 (1991), 175-185.
doi: 10.1007/BF02540222. |
[22] |
H. A. Levine and B. D. Sleeman,
A system of reaction diffusion equation arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57 (1997), 683-730.
doi: 10.1137/S0036139995291106. |
[23] |
H. A. Levine and J. Renclawowicz,
Singularity formation in chemotaxis - a conjecture of
nagai, SIAM J. Appl. Math., 65 (2004), 336-360.
doi: 10.1137/S0036139903431725. |
[24] |
H. A. Levine, B. P. Sleeman and N. Nilsen-Hamilton,
A mathematical modeling for the roles
of pericytes and macrophages in the initiation of angiogenesis I. The role of protease inhibitors
in preventing angiogenesis, Mathematical Biosciences, 168 (2000), 75-115.
doi: 10.1016/S0025-5564(00)00034-1. |
[25] |
Y. Li, K. Lin and C. Mu,
Boundedness and asymptotic behavior of solutions to a chemotaxishaptotaxis model in high dimensions, Applied Mathematics Letters, 50 (2015), 91-97.
doi: 10.1016/j.aml.2015.06.010. |
[26] |
M. Malogrosz,
Well-posedness and asymptotic behavior of a multidimensonal model of morphogen transport, J. Evol. Eq., 12 (2012), 353-366.
doi: 10.1007/s00028-012-0135-5. |
[27] |
M. Małogrosz,
A model of morphogen transport in the presence of glypicans II, Journal of Mathematical Analysis and Applications, 433 (2016), 642-680.
doi: 10.1016/j.jmaa.2015.07.053. |
[28] |
J. H. Merking, D. J. Needham and B. D. Sleeman,
A mathematical model for the spread of
morphogens with density dependent chemosensitivity, Nonlinearity, 18 (2005), 2745-2773.
doi: 10.1088/0951-7715/18/6/018. |
[29] |
J. H. Merking and B. D. Sleeman,
On the spread of morphogens, J. Math. Biol., 51 (2005), 1-17.
doi: 10.1007/s00285-004-0308-0. |
[30] |
M. Mizukami and T. Yokota,
Global existence and asymptotic stability of solutions to a twospecies chemotaxis system with any chemical diffusion, J. Differential Equations, 261 (2016), 2650-2669.
doi: 10.1016/j.jde.2016.05.008. |
[31] |
A.I. Muñoz and J. I. Tello,
Mathematical analysis and numerical simulation of a model of morphogenesis, Mathematical Biosciences and Engineering, 8 (2011), 1035-1059.
doi: 10.3934/mbe.2011.8.1035. |
[32] |
M. Negreanu and J. I. Tello,
On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., 46 (2014), 3761-3781.
doi: 10.1137/140971853. |
[33] |
M. Negreanu and J. I. Tello,
On a comparison method to reaction-diffusion systems and its
applications to chemotaxis, Discrete and Continuous Dynamical Systems-Series B, 18 (2013), 2669-2688.
doi: 10.3934/dcdsb.2013.18.2669. |
[34] |
M. Negreanu and J. I. Tello,
On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., 46 (2014), 3761-3781.
doi: 10.1137/140971853. |
[35] |
M. Negreanu and J. I. Tello,
Asymptotic stability of a two species chemotaxis system with
non-diffusive chemoattractant, J. Differential Equations, 258 (2015), 1592-1617.
doi: 10.1016/j.jde.2014.11.009. |
[36] |
C. S. Patlak,
Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, 15 (1953), 311-338.
doi: 10.1007/BF02476407. |
[37] |
H. G. Othmer and A. Stevens,
Aggregation, blowup, and collapse: The ABC$^{\prime}$s of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), 1044-1081.
|
[38] |
B. D. Sleeman and H. A. Levine,
Partial differential equations of chemotaxis and angiogenesis, Math. Methods Appl. Sci., 24 (2001), 405-426.
doi: 10.1002/mma.212. |
[39] |
B. D. Sleeman and H. A. Levine,
Partial differential equations of chemotaxis and angiogenesis, SIAM J. Appl. Math., 65 (2005), 790-817.
doi: 10.1137/S0036139902415117. |
[40] |
A. Stevens,
The derivation of chemotaxis equations as limit dynamics of moderately interacting stochactic many-particle systems, SIAM J. Appl. Math., 61 (2000), 183-212.
doi: 10.1137/S0036139998342065. |
[41] |
C. Stinner, J. I. Tello and M. Winkler,
Mathematical analysis of a model of chemotaxis arising from morphogenesis, Math. Methods Appl. Sci., 35 (2012), 445-465.
doi: 10.1002/mma.1573. |
[42] |
C. Stinner, J. I. Tello and M. Winkler,
Competitive exclusion in a two-species chemotaxis
model, Journal of Mathematical Biology, 68 (2014), 1607-1626.
doi: 10.1007/s00285-013-0681-7. |
[43] |
T. Suzuki,
Mathematical models of tumor growth systems, Mathematica Bohemica, 137 (2012), 201-218.
|
[44] |
T. Suzuki and R. Takahashi,
Global in time solution to a class of tumour growth systems, Adv. Math. Sci. Appl., 19 (2009), 503-524.
|
[45] |
J. I. Tello,
Mathematical analysis of a model of Morphogenesis, Discrete and Continuous Dynamical Systems - Serie A., 25 (2009), 343-361.
doi: 10.3934/dcds.2009.25.343. |
[46] |
J. I. Tello and M. Winkler,
Stabilization in a two-species chemotaxis system with a logistic
source, Nonlinearity, 25 (2012), 1413-1425.
doi: 10.1088/0951-7715/25/5/1413. |
[47] |
A. M. Turing,
The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society of London, Series B, 237 (1952), 37-72.
doi: 10.1098/rstb.1952.0012. |
[48] |
X. Wang and Y. Wu,
Qualitative analysis on a chemotactic diffusion model for two species
competing for a limited resource, Quart. Appl. Math., 60 (2002), 505-531.
doi: 10.1090/qam/1914439. |
[1] |
Ling Liu, Jiashan Zheng. Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3357-3377. doi: 10.3934/dcdsb.2018324 |
[2] |
Karl Kunisch, Sérgio S. Rodrigues. Oblique projection based stabilizing feedback for nonautonomous coupled parabolic-ode systems. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6355-6389. doi: 10.3934/dcds.2019276 |
[3] |
Tomasz Cieślak, Kentarou Fujie. Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 165-176. doi: 10.3934/dcdss.2020009 |
[4] |
T. Hillen, K. Painter, Christian Schmeiser. Global existence for chemotaxis with finite sampling radius. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 125-144. doi: 10.3934/dcdsb.2007.7.125 |
[5] |
Mengyao Ding, Wei Wang. Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4665-4684. doi: 10.3934/dcdsb.2018328 |
[6] |
Wei Wang, Yan Li, Hao Yu. Global boundedness in higher dimensions for a fully parabolic chemotaxis system with singular sensitivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3663-3669. doi: 10.3934/dcdsb.2017147 |
[7] |
Ke Lin, Chunlai Mu. Global dynamics in a fully parabolic chemotaxis system with logistic source. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5025-5046. doi: 10.3934/dcds.2016018 |
[8] |
Daniela Giachetti, Maria Michaela Porzio. Global existence for nonlinear parabolic equations with a damping term. Communications on Pure and Applied Analysis, 2009, 8 (3) : 923-953. doi: 10.3934/cpaa.2009.8.923 |
[9] |
Sainan Wu, Junping Shi, Boying Wu. Global existence of solutions to an attraction-repulsion chemotaxis model with growth. Communications on Pure and Applied Analysis, 2017, 16 (3) : 1037-1058. doi: 10.3934/cpaa.2017050 |
[10] |
Huanhuan Qiu, Shangjiang Guo. Global existence and stability in a two-species chemotaxis system. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1569-1587. doi: 10.3934/dcdsb.2018220 |
[11] |
Radek Erban, Hyung Ju Hwang. Global existence results for complex hyperbolic models of bacterial chemotaxis. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1239-1260. doi: 10.3934/dcdsb.2006.6.1239 |
[12] |
Abelardo Duarte-Rodríguez, Lucas C. F. Ferreira, Élder J. Villamizar-Roa. Global existence for an attraction-repulsion chemotaxis fluid model with logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 423-447. doi: 10.3934/dcdsb.2018180 |
[13] |
Johannes Lankeit, Yulan Wang. Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6099-6121. doi: 10.3934/dcds.2017262 |
[14] |
Guoqiang Ren, Heping Ma. Global existence in a chemotaxis system with singular sensitivity and signal production. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 343-360. doi: 10.3934/dcdsb.2021045 |
[15] |
Etsushi Nakaguchi, Koichi Osaki. Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2627-2646. doi: 10.3934/dcdsb.2013.18.2627 |
[16] |
Rachidi B. Salako, Wenxian Shen. Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 293-319. doi: 10.3934/dcdss.2020017 |
[17] |
Francesca R. Guarguaglini. Global solutions for a chemotaxis hyperbolic-parabolic system on networks with nonhomogeneous boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1057-1087. doi: 10.3934/cpaa.2020049 |
[18] |
Hong Yi, Chunlai Mu, Shuyan Qiu, Lu Xu. Global boundedness of radial solutions to a parabolic-elliptic chemotaxis system with flux limitation and nonlinear signal production. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3825-3849. doi: 10.3934/cpaa.2021133 |
[19] |
Zhengce Zhang, Yan Li. Global existence and gradient blowup of solutions for a semilinear parabolic equation with exponential source. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 3019-3029. doi: 10.3934/dcdsb.2014.19.3019 |
[20] |
Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]