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]

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
[2]

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
[3]

Chris Cosner. Reaction-diffusion-advection models for the effects and evolution of dispersal. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1701-1745. doi: 10.3934/dcds.2014.34.1701
[4]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989
[5]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3841-3859. doi: 10.3934/dcds.2012.32.3841
[6]

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
[7]

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
[8]

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
[9]

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
[10]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. Determination of initial data for a reaction-diffusion system with variable coefficients. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 771-801. doi: 10.3934/dcds.2019032
[11]

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
[12]

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 - A, 2007, 18 (2&3) : 537-567. doi: 10.3934/dcds.2007.18.537
[13]

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
[14]

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
[15]

Congming Li, Eric S. Wright. Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics. Communications on Pure & Applied Analysis, 2002, 1 (1) : 77-84. doi: 10.3934/cpaa.2002.1.77
[16]

Erik Kropat, Silja Meyer-Nieberg, Gerhard-Wilhelm Weber. Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure -- efficient solution strategies based on homogenization theory. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 183-219. doi: 10.3934/naco.2016008
[17]

Takashi Kajiwara. A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2133-2156. doi: 10.3934/cpaa.2017106
[18]

Andrea L. Bertozzi, Dejan Slepcev. Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1617-1637. doi: 10.3934/cpaa.2010.9.1617
[19]

Vicent Caselles. An existence and uniqueness result for flux limited diffusion equations. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1151-1195. doi: 10.3934/dcds.2011.31.1151
[20]

Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (24)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences