March  2006, 5(1): 97-106. doi: 10.3934/cpaa.2006.5.97

The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system

1. 

Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan

2. 

Graduate School of Mathematics, Hiroshima University, Hiroshima, 739-8526, Japan

3. 

Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578

Received  September 2004 Revised  October 2005 Published  December 2005

In this paper, we discuss the global existence and uniform boundedness of the radial solutions to the drift-diffusion system in two space dimension, which is derived from the simulation of semiconductor device design and self-interacting particles. It is shown that the time global existence and the uniform boundedness of the solution to the problem below the sharp threshold condition.
Citation: Masaki Kurokiba, Toshitaka Nagai, T. Ogawa. The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system. Communications on Pure & Applied Analysis, 2006, 5 (1) : 97-106. doi: 10.3934/cpaa.2006.5.97
[1]

Elio E. Espejo, Masaki Kurokiba, Takashi Suzuki. Blowup threshold and collapse mass separation for a drift-diffusion system in space-dimension two. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2627-2644. doi: 10.3934/cpaa.2013.12.2627

[2]

Takayoshi Ogawa, Hiroshi Wakui. Stability and instability of solutions to the drift-diffusion system. Evolution Equations & Control Theory, 2017, 6 (4) : 587-597. doi: 10.3934/eect.2017029

[3]

T. Ogawa. The degenerate drift-diffusion system with the Sobolev critical exponent. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 875-886. doi: 10.3934/dcdss.2011.4.875

[4]

Ronald E. Mickens. A nonstandard finite difference scheme for the drift-diffusion system. Conference Publications, 2009, 2009 (Special) : 558-563. doi: 10.3934/proc.2009.2009.558

[5]

Claire Chainais-Hillairet, Ingrid Lacroix-Violet. On the existence of solutions for a drift-diffusion system arising in corrosion modeling. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 77-92. doi: 10.3934/dcdsb.2015.20.77

[6]

Corrado Lattanzio, Pierangelo Marcati. The relaxation to the drift-diffusion system for the 3-$D$ isentropic Euler-Poisson model for semiconductors. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 449-455. doi: 10.3934/dcds.1999.5.449

[7]

H.J. Hwang, K. Kang, A. Stevens. Drift-diffusion limits of kinetic models for chemotaxis: A generalization. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 319-334. doi: 10.3934/dcdsb.2005.5.319

[8]

Dietmar Oelz, Alex Mogilner. A drift-diffusion model for molecular motor transport in anisotropic filament bundles. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4553-4567. doi: 10.3934/dcds.2016.36.4553

[9]

Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825

[10]

Clément Jourdana, Paola Pietra. A quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures. Kinetic & Related Models, 2019, 12 (1) : 217-242. doi: 10.3934/krm.2019010

[11]

Marcel Freitag. Global existence and boundedness in a chemorepulsion system with superlinear diffusion. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5943-5961. doi: 10.3934/dcds.2018258

[12]

Cyrill B. Muratov, Xing Zhong. Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 915-944. doi: 10.3934/dcds.2017038

[13]

Pan Zheng, Chunlai Mu, Xiaojun Song. On the boundedness and decay of solutions for a chemotaxis-haptotaxis system with nonlinear diffusion. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1737-1757. doi: 10.3934/dcds.2016.36.1737

[14]

Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395

[15]

Fuchen Zhang, Xiaofeng Liao, Chunlai Mu, Guangyun Zhang, Yi-An Chen. On global boundedness of the Chen system. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1673-1681. doi: 10.3934/dcdsb.2017080

[16]

Pan Zheng. Global boundedness and decay for a multi-dimensional chemotaxis-haptotaxis system with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 2039-2056. doi: 10.3934/dcdsb.2016035

[17]

Inwon C. Kim, Helen K. Lei. Degenerate diffusion with a drift potential: A viscosity solutions approach. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 767-786. doi: 10.3934/dcds.2010.27.767

[18]

Hai-Yang Jin. Boundedness and large time behavior in a two-dimensional Keller-Segel-Navier-Stokes system with signal-dependent diffusion and sensitivity. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3595-3616. doi: 10.3934/dcds.2018155

[19]

Simona Fornaro, Stefano Lisini, Giuseppe Savaré, Giuseppe Toscani. Measure valued solutions of sub-linear diffusion equations with a drift term. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1675-1707. doi: 10.3934/dcds.2012.32.1675

[20]

Sallah Eddine Boutiah, Abdelaziz Rhandi, Cristian Tacelli. Kernel estimates for elliptic operators with unbounded diffusion, drift and potential terms. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 803-817. doi: 10.3934/dcds.2019033

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]