American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Global solution to a phase transition model with microscopic movements and accelerations in one space dimension
  • CPAA Home
  • This Issue
  • Next Article
    On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations
December  2006, 5(4): 733-762. doi: 10.3934/cpaa.2006.5.733

Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data

Mostafa Bendahmane 1, and  Kenneth H. Karlsen 1,

1. 

Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway

Received  September 2004 Revised  February 2005 Published  September 2006

We prove existence of a renormalized solution to a system of nonlinear partial differential equations with anisotropic diffusivities and transport effects, supplemented with initial and Dirichlet boundary conditions. The data are assumed to be merely integrable. This system models the spread of an epidemic disease through a heterogeneous habitat.
Keywords: uniqueness., anisotropic diffusion, existence, Reaction-diffusion-advection system, integrable data, renormalized solution.
Mathematics Subject Classification: Primary: 35K57, 35K55, 92D3.
Citation: Mostafa Bendahmane, Kenneth H. Karlsen. Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data. Communications on Pure & Applied Analysis, 2006, 5 (4) : 733-762. doi: 10.3934/cpaa.2006.5.733
[1]

Bo Duan, Zhengce Zhang. A two-species weak competition system of reaction-diffusion-advection with double free boundaries. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 801-829. doi: 10.3934/dcdsb.2018208
[2]

Linfeng Mei, Xiaoyan Zhang. On a nonlocal reaction-diffusion-advection system modeling phytoplankton growth with light and nutrients. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 221-243. doi: 10.3934/dcdsb.2012.17.221
[3]

Baifeng Zhang, Guohong Zhang, Xiaoli Wang. Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021260
[4]

Bo Duan, Zhengce Zhang. A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2022, 27 (2) : 837-861. doi: 10.3934/dcdsb.2021067
[5]

Chris Cosner. Reaction-diffusion-advection models for the effects and evolution of dispersal. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 1701-1745. doi: 10.3934/dcds.2014.34.1701
[6]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989
[7]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems, 2012, 32 (11) : 3841-3859. doi: 10.3934/dcds.2012.32.3841
[8]

Qiang Liu, Zhichang Guo, Chunpeng Wang. Renormalized solutions to a reaction-diffusion system applied to image denoising. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1839-1858. doi: 10.3934/dcdsb.2016025
[9]

Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217
[10]

Danhua Jiang, Zhi-Cheng Wang, Liang Zhang. A reaction-diffusion-advection SIS epidemic model in a spatially-temporally heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4557-4578. doi: 10.3934/dcdsb.2018176
[11]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
[12]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017
[13]

Chengxia Lei, Xinhui Zhou. Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021174
[14]

Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326
[15]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. Determination of initial data for a reaction-diffusion system with variable coefficients. Discrete & Continuous Dynamical Systems, 2019, 39 (2) : 771-801. doi: 10.3934/dcds.2019032
[16]

Michaël Bages, Patrick Martinez. Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 817-869. doi: 10.3934/dcdsb.2010.14.817
[17]

Kwangjoong Kim, Wonhyung Choi, Inkyung Ahn. Reaction-advection-diffusion competition models under lethal boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021250
[18]

Aníbal Rodríguez-Bernal, Alejandro Vidal–López. Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 537-567. doi: 10.3934/dcds.2007.18.537
[19]

Alexey Cheskidov, Songsong Lu. The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 55-66. doi: 10.3934/dcdss.2009.2.55
[20]

Dominique Blanchard, Nicolas Bruyère, Olivier Guibé. Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2213-2227. doi: 10.3934/cpaa.2013.12.2213

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (84)
  • HTML views (0)
  • Cited by (35)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy