October  2010, 14(3): 1211-1236. doi: 10.3934/dcdsb.2010.14.1211

Anti-shifting phenomenon of a convective nonlinear diffusion equation

1. 

School of Mathematics, Jilin University, Changchun 130012, China

2. 

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

3. 

School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China

Received  April 2008 Revised  November 2009 Published  July 2010

This paper concerns a convective nonlinear diffusion equation which is strongly degenerate. The existence and uniqueness of the $BV$ solution to the initial-boundary problem are proved. Then we deal with the anti-shifting phenomenon by investigating the corresponding free boundary problem. As a consequence, it is possible to find a suitable convection such that the discontinuous point of the solution remains unmoved.
Citation: Chunpeng Wang, Jingxue Yin, Bibo Lu. Anti-shifting phenomenon of a convective nonlinear diffusion equation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1211-1236. doi: 10.3934/dcdsb.2010.14.1211
[1]

Chengxia Lei, Yihong Du. Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 895-911. doi: 10.3934/dcdsb.2017045

[2]

Ahmad El Hajj, Hassan Ibrahim, Vivian Rizik. $ BV $ solution for a non-linear Hamilton-Jacobi system. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3273-3293. doi: 10.3934/dcds.2020405

[3]

Minhajul, T. Raja Sekhar, G. P. Raja Sekhar. Stability of solutions to the Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3367-3386. doi: 10.3934/cpaa.2019152

[4]

Anupam Sen, T. Raja Sekhar. Delta shock wave and wave interactions in a thin film of a perfectly soluble anti-surfactant solution. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2641-2653. doi: 10.3934/cpaa.2020115

[5]

Xiaoli Li. Global strong solution for the incompressible flow of liquid crystals with vacuum in dimension two. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 4907-4922. doi: 10.3934/dcds.2017211

[6]

Nguyen Ba Minh, Pham Huu Sach. Strong vector equilibrium problems with LSC approximate solution mappings. Journal of Industrial & Management Optimization, 2020, 16 (2) : 511-529. doi: 10.3934/jimo.2018165

[7]

Kenji Kimura, Jen-Chih Yao. Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 167-181. doi: 10.3934/jimo.2008.4.167

[8]

Stefano Bianchini, Daniela Tonon. A decomposition theorem for $BV$ functions. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1549-1566. doi: 10.3934/cpaa.2011.10.1549

[9]

Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917

[10]

Yongfu Wang. Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier-Stokes flows with vacuum. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4317-4333. doi: 10.3934/dcdsb.2020099

[11]

Lihuai Du, Ting Zhang. Local and global strong solution to the stochastic 3-D incompressible anisotropic Navier-Stokes equations. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4745-4765. doi: 10.3934/dcds.2018209

[12]

Xin Zhong. Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3563-3578. doi: 10.3934/dcdsb.2020246

[13]

Jishan Fan, Fucai Li, Gen Nakamura. Global strong solution to the two-dimensional density-dependent magnetohydrodynamic equations with vaccum. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1481-1490. doi: 10.3934/cpaa.2014.13.1481

[14]

Lam Quoc Anh, Nguyen Van Hung. Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. Journal of Industrial & Management Optimization, 2018, 14 (1) : 65-79. doi: 10.3934/jimo.2017037

[15]

Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (10) : 5383-5405. doi: 10.3934/dcdsb.2020348

[16]

Yu-Xia Wang, Wan-Tong Li. Spatial degeneracy vs functional response. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2811-2837. doi: 10.3934/dcdsb.2016074

[17]

Linhe Zhu, Wenshan Liu. Spatial dynamics and optimization method for a network propagation model in a shifting environment. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1843-1874. doi: 10.3934/dcds.2020342

[18]

Yueding Yuan, Yang Wang, Xingfu Zou. Spatial dynamics of a Lotka-Volterra model with a shifting habitat. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5633-5671. doi: 10.3934/dcdsb.2019076

[19]

Alberto Bressan, Wen Shen. BV estimates for multicomponent chromatography with relaxation. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 21-38. doi: 10.3934/dcds.2000.6.21

[20]

Adriana C. Briozzo, María F. Natale, Domingo A. Tarzia. The Stefan problem with temperature-dependent thermal conductivity and a convective term with a convective condition at the fixed face. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1209-1220. doi: 10.3934/cpaa.2010.9.1209

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (43)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]