American Institute of Mathematical Sciences

• Previous Article
Constrained stability and instability of polynomial difference equations with state-dependent noise
• DCDS-B Home
• This Issue
• Next Article
Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos
June  2009, 11(4): 935-970. doi: 10.3934/dcdsb.2009.11.935

On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder

 1 Narvik University College, Postbox 385, 8505 Narvik, Norway, Norway

Received  June 2008 Revised  September 2008 Published  April 2009

The work focuses on the behaviour at infinity of solutions to second order elliptic equation with first order terms in a semi-infinite cylinder. Neumann's boundary condition is imposed on the lateral boundary of the cylinder and Dirichlet condition on its base. Under the assumption that the coefficients stabilize to a periodic regime, we prove the existence of a bounded solution, its stabilization to a constant, and provide necessary and sufficient condition for the uniqueness.
Citation: Iryna Pankratova, Andrey Piatnitski. On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 935-970. doi: 10.3934/dcdsb.2009.11.935
 [1] Yanqun Liu, Ming-Fang Ding. A ladder method for linear semi-infinite programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 397-412. doi: 10.3934/jimo.2014.10.397 [2] Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions. Inverse Problems & Imaging, 2008, 2 (3) : 317-333. doi: 10.3934/ipi.2008.2.317 [3] Alexander L. Skubachevskii. Nonlocal elliptic problems in infinite cylinder and applications. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 847-868. doi: 10.3934/dcdss.2016032 [4] Jinchuan Zhou, Naihua Xiu, Jein-Shan Chen. Solution properties and error bounds for semi-infinite complementarity problems. Journal of Industrial & Management Optimization, 2013, 9 (1) : 99-115. doi: 10.3934/jimo.2013.9.99 [5] Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial & Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705 [6] Burcu Özçam, Hao Cheng. A discretization based smoothing method for solving semi-infinite variational inequalities. Journal of Industrial & Management Optimization, 2005, 1 (2) : 219-233. doi: 10.3934/jimo.2005.1.219 [7] Iryna Pankratova, Andrey Piatnitski. Homogenization of convection-diffusion equation in infinite cylinder. Networks & Heterogeneous Media, 2011, 6 (1) : 111-126. doi: 10.3934/nhm.2011.6.111 [8] Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva. Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems. Inverse Problems & Imaging, 2012, 6 (4) : 599-621. doi: 10.3934/ipi.2012.6.599 [9] Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semi-infinite programming with projected Newton-type algorithm. Journal of Industrial & Management Optimization, 2009, 5 (1) : 141-151. doi: 10.3934/jimo.2009.5.141 [10] Jinchuan Zhou, Changyu Wang, Naihua Xiu, Soonyi Wu. First-order optimality conditions for convex semi-infinite min-max programming with noncompact sets. Journal of Industrial & Management Optimization, 2009, 5 (4) : 851-866. doi: 10.3934/jimo.2009.5.851 [11] Igor Chueshov. Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions. Evolution Equations & Control Theory, 2016, 5 (4) : 561-566. doi: 10.3934/eect.2016019 [12] Meixia Li, Changyu Wang, Biao Qu. Non-convex semi-infinite min-max optimization with noncompact sets. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1859-1881. doi: 10.3934/jimo.2017022 [13] Xiaodong Fan, Tian Qin. Stability analysis for generalized semi-infinite optimization problems under functional perturbations. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2018201 [14] Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1007-1015. doi: 10.3934/dcdss.2020059 [15] Luis Caffarelli, Juan-Luis Vázquez. Asymptotic behaviour of a porous medium equation with fractional diffusion. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1393-1404. doi: 10.3934/dcds.2011.29.1393 [16] Atul Kumar, R. R. Yadav. Analytical approach of one-dimensional solute transport through inhomogeneous semi-infinite porous domain for unsteady flow: Dispersion being proportional to square of velocity. Conference Publications, 2013, 2013 (special) : 457-466. doi: 10.3934/proc.2013.2013.457 [17] Tomás Caraballo, María J. Garrido–Atienza, Björn Schmalfuss, José Valero. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 439-455. doi: 10.3934/dcdsb.2010.14.439 [18] Gabriele Grillo, Matteo Muratori, Fabio Punzo. On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 5927-5962. doi: 10.3934/dcds.2015.35.5927 [19] Abdelaziz Rhandi, Roland Schnaubelt. Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 663-683. doi: 10.3934/dcds.1999.5.663 [20] Jun Bao, Lihe Wang, Chunqin Zhou. Positive solutions to elliptic equations in unbounded cylinder. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1389-1400. doi: 10.3934/dcdsb.2016001

2018 Impact Factor: 1.008