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Positive entropic schemes for a nonlinear fourthorder parabolic equation
Instability of planar traveling waves in bistable reactiondiffusion systems
1.  Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan 
[1] 
Judith R. Miller, Huihui Zeng. Multidimensional stability of planar traveling waves for an integrodifference model. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 741751. doi: 10.3934/dcdsb.2013.18.741 
[2] 
Zhaohai Ma, Rong Yuan, Yang Wang, Xin Wu. Multidimensional stability of planar traveling waves for the delayed nonlocal dispersal competitive LotkaVolterra system. Communications on Pure & Applied Analysis, 2019, 18 (4) : 20692092. doi: 10.3934/cpaa.2019093 
[3] 
Grégory Faye. Multidimensional stability of planar traveling waves for the scalar nonlocal AllenCahn equation. Discrete & Continuous Dynamical Systems  A, 2016, 36 (5) : 24732496. doi: 10.3934/dcds.2016.36.2473 
[4] 
Rui Huang, Ming Mei, Yong Wang. Planar traveling waves for nonlocal dispersion equation with monostable nonlinearity. Discrete & Continuous Dynamical Systems  A, 2012, 32 (10) : 36213649. doi: 10.3934/dcds.2012.32.3621 
[5] 
Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure & Applied Analysis, 2011, 10 (1) : 141160. doi: 10.3934/cpaa.2011.10.141 
[6] 
Fengxin Chen. Stability and uniqueness of traveling waves for system of nonlocal evolution equations with bistable nonlinearity. Discrete & Continuous Dynamical Systems  A, 2009, 24 (3) : 659673. doi: 10.3934/dcds.2009.24.659 
[7] 
Yaping Wu, Niannian Yan. Stability of traveling waves for autocatalytic reaction systems with strong decay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (4) : 16011633. doi: 10.3934/dcdsb.2017033 
[8] 
Grigori Chapiro, Lucas Furtado, Dan Marchesin, Stephen Schecter. Stability of interacting traveling waves in reactionconvectiondiffusion systems. Conference Publications, 2015, 2015 (special) : 258266. doi: 10.3934/proc.2015.0258 
[9] 
JeChiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete & Continuous Dynamical Systems  A, 2008, 21 (2) : 601623. doi: 10.3934/dcds.2008.21.601 
[10] 
Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete & Continuous Dynamical Systems  B, 2012, 17 (3) : 9931007. doi: 10.3934/dcdsb.2012.17.993 
[11] 
Judith R. Miller, Huihui Zeng. Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology. Discrete & Continuous Dynamical Systems  B, 2011, 16 (3) : 895925. doi: 10.3934/dcdsb.2011.16.895 
[12] 
Tong Li, Jeungeun Park. Stability of traveling waves of models for image processing with nonconvex nonlinearity. Communications on Pure & Applied Analysis, 2018, 17 (3) : 959985. doi: 10.3934/cpaa.2018047 
[13] 
XiaoBiao Lin, Stephen Schecter. Traveling waves and shock waves. Discrete & Continuous Dynamical Systems  A, 2004, 10 (4) : iii. doi: 10.3934/dcds.2004.10.4i 
[14] 
WeiJie Sheng, WanTong Li. Multidimensional stability of timeperiodic planar traveling fronts in bistable reactiondiffusion equations. Discrete & Continuous Dynamical Systems  A, 2017, 37 (5) : 26812704. doi: 10.3934/dcds.2017115 
[15] 
Yoshihiro Ueda, Tohru Nakamura, Shuichi Kawashima. Stability of planar stationary waves for damped wave equations with nonlinear convection in multidimensional half space. Kinetic & Related Models, 2008, 1 (1) : 4964. doi: 10.3934/krm.2008.1.49 
[16] 
Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang. Asymptotic stability of nonmonotone traveling waves for timedelayed nonlocal dispersion equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (3) : 13311353. doi: 10.3934/dcds.2016.36.1331 
[17] 
ZhaoXing Yang, GuoBao Zhang, Ge Tian, Zhaosheng Feng. Stability of nonmonotone noncritical traveling waves in discrete reactiondiffusion equations with time delay. Discrete & Continuous Dynamical Systems  S, 2017, 10 (3) : 581603. doi: 10.3934/dcdss.2017029 
[18] 
Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 561569. doi: 10.3934/dcds.2009.23.561 
[19] 
Yicheng Jiang, Kaijun Zhang. Stability of traveling waves for nonlocal timedelayed reactiondiffusion equations. Kinetic & Related Models, 2018, 11 (5) : 12351253. doi: 10.3934/krm.2018048 
[20] 
Luyi Ma, HongTao Niu, ZhiCheng Wang. Global asymptotic stability of traveling waves to the AllenCahn equation with a fractional Laplacian. Communications on Pure & Applied Analysis, 2019, 18 (5) : 24572472. doi: 10.3934/cpaa.2019111 
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