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Existence result for a mixture of non Newtonian flows with stress diffusion using the CahnHilliard formulation
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] 
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 
[3] 
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 
[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] 
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 
[7] 
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 
[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] 
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 
[14] 
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 
[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] 
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 
[18] 
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 
[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] 
Yaping Wu, Xiuxia Xing. Stability of traveling waves with critical speeds for $P$degree Fishertype equations. Discrete & Continuous Dynamical Systems  A, 2008, 20 (4) : 11231139. doi: 10.3934/dcds.2008.20.1123 
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