• Previous Article
    On a comparison method to reaction-diffusion systems and its applications to chemotaxis
  • DCDS-B Home
  • This Issue
  • Next Article
    Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation
December  2013, 18(10): 2647-2668. doi: 10.3934/dcdsb.2013.18.2647

Well-posedness for a model of individual clustering

1. 

Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse cedex 9

Received  November 2012 Revised  February 2013 Published  October 2013

We study the well-posedness of a model of individual clustering. Given $p>N\geq 1$ and an initial condition in $W^{1,p}(\Omega)$, the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction rates and show global existence if $N=1$, as well as, the convergence to steady states for one of these rates.
Citation: Elissar Nasreddine. Well-posedness for a model of individual clustering. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2647-2668. doi: 10.3934/dcdsb.2013.18.2647
References:
[1]

Oxford Lecture Series in Mathematics and it Applications, 2006. Google Scholar

[2]

Parabolic and Navier-Stokes Equations, Part 1, 105-117, Banach Center Publ., 81, Part 1, Polish Acad. Sci. Inst. Math., Warsaw, 2008. doi: 10.4064/bc81-0-7.  Google Scholar

[3]

J. Math. Anal. Appl., 67 (1979), 525-541. doi: 10.1016/0022-247X(79)90041-6.  Google Scholar

[4]

Bolletino, U. M. I.(5), 16 (1979), 22-31.  Google Scholar

[5]

J. Math. Biol., 26 (1988), 651-660. doi: 10.1007/BF00276146.  Google Scholar

[6]

Providence (R. I.) , American Mathematical Society, 1988. Google Scholar

[7]

Nonlinear Anal., 9 (1985), 321-333. doi: 10.1016/0362-546X(85)90057-4.  Google Scholar

[8]

(French) Ann. Fac. Sci. Toulouse Math. (5), 2 (1980), 125-135. doi: 10.5802/afst.550.  Google Scholar

[9]

Annali di Mathematica Pura ed Applicata (IV), 146 (1987), 65-69. doi: 10.1007/BF01762360.  Google Scholar

show all references

References:
[1]

Oxford Lecture Series in Mathematics and it Applications, 2006. Google Scholar

[2]

Parabolic and Navier-Stokes Equations, Part 1, 105-117, Banach Center Publ., 81, Part 1, Polish Acad. Sci. Inst. Math., Warsaw, 2008. doi: 10.4064/bc81-0-7.  Google Scholar

[3]

J. Math. Anal. Appl., 67 (1979), 525-541. doi: 10.1016/0022-247X(79)90041-6.  Google Scholar

[4]

Bolletino, U. M. I.(5), 16 (1979), 22-31.  Google Scholar

[5]

J. Math. Biol., 26 (1988), 651-660. doi: 10.1007/BF00276146.  Google Scholar

[6]

Providence (R. I.) , American Mathematical Society, 1988. Google Scholar

[7]

Nonlinear Anal., 9 (1985), 321-333. doi: 10.1016/0362-546X(85)90057-4.  Google Scholar

[8]

(French) Ann. Fac. Sci. Toulouse Math. (5), 2 (1980), 125-135. doi: 10.5802/afst.550.  Google Scholar

[9]

Annali di Mathematica Pura ed Applicata (IV), 146 (1987), 65-69. doi: 10.1007/BF01762360.  Google Scholar

[1]

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

[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]

Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196

[4]

Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184

[5]

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

[6]

Fabio Sperotto Bemfica, Marcelo Mendes Disconzi, Casey Rodriguez, Yuanzhen Shao. Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021069

[7]

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

[8]

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

[9]

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

[10]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[11]

Izumi Takagi, Conghui Zhang. Existence and stability of patterns in a reaction-diffusion-ODE system with hysteresis in non-uniform media. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3109-3140. doi: 10.3934/dcds.2020400

[12]

Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810

[13]

Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973

[14]

Shu-Yu Hsu. Existence and properties of ancient solutions of the Yamabe flow. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 91-129. doi: 10.3934/dcds.2018005

[15]

Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure & Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513

[16]

Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017

[17]

Yuta Ishii, Kazuhiro Kurata. Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021035

[18]

Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steady-state and first passage time distributions for waiting times in the $ MAP/M/s+G $ queueing model with generally distributed patience times. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021078

[19]

José Raúl Quintero, Juan Carlos Muñoz Grajales. On the existence and computation of periodic travelling waves for a 2D water wave model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 557-578. doi: 10.3934/cpaa.2018030

[20]

Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]