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An Evans function approach to spectral stability of smallamplitude shock profiles
A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium
1.  Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States 
[1] 
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 
[2] 
Hongmei Cheng, Rong Yuan. Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 30073022. doi: 10.3934/dcdsb.2017160 
[3] 
Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 15071522. doi: 10.3934/dcdsb.2014.19.1507 
[4] 
ChengHsiung Hsu, JianJhong Lin. Stability analysis of traveling wave solutions for lattice reactiondiffusion equations. Discrete & Continuous Dynamical Systems  B, 2020, 25 (5) : 17571774. doi: 10.3934/dcdsb.2020001 
[5] 
Min He. A class of integrodifferential equations and applications. Conference Publications, 2005, 2005 (Special) : 386396. doi: 10.3934/proc.2005.2005.386 
[6] 
Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure & Applied Analysis, 2015, 14 (4) : 13571376. doi: 10.3934/cpaa.2015.14.1357 
[7] 
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 
[8] 
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 
[9] 
Xiaoxiao Zheng, Hui Wu. Orbital stability of periodic traveling wave solutions to the coupled compound KdV and MKdV equations with two components. Mathematical Foundations of Computing, 2020, 3 (1) : 1124. doi: 10.3934/mfc.2020002 
[10] 
Guangying Lv, Mingxin Wang. Existence, uniqueness and stability of traveling wave fronts of discrete quasilinear equations with delay. Discrete & Continuous Dynamical Systems  B, 2010, 13 (2) : 415433. doi: 10.3934/dcdsb.2010.13.415 
[11] 
Xiaojie Hou, Yi Li. Local stability of travelingwave solutions of nonlinear reactiondiffusion equations. Discrete & Continuous Dynamical Systems  A, 2006, 15 (2) : 681701. doi: 10.3934/dcds.2006.15.681 
[12] 
Mathias Nikolai Arnesen. Existence of solitarywave solutions to nonlocal equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (7) : 34833510. doi: 10.3934/dcds.2016.36.3483 
[13] 
Stephan Didas, Joachim Weickert. Integrodifferential equations for continuous multiscale wavelet shrinkage. Inverse Problems & Imaging, 2007, 1 (1) : 4762. doi: 10.3934/ipi.2007.1.47 
[14] 
Paola Loreti, Daniela Sforza. Inverse observability inequalities for integrodifferential equations in square domains. Evolution Equations & Control Theory, 2018, 7 (1) : 6177. doi: 10.3934/eect.2018004 
[15] 
Weiran Sun, Min Tang. A relaxation method for one dimensional traveling waves of singular and nonlocal equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (5) : 14591491. doi: 10.3934/dcdsb.2013.18.1459 
[16] 
Albert Erkip, Abba I. Ramadan. Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. Communications on Pure & Applied Analysis, 2017, 16 (6) : 21252132. doi: 10.3934/cpaa.2017105 
[17] 
Linghai Zhang. Wave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networks. Discrete & Continuous Dynamical Systems  A, 2014, 34 (5) : 24052450. doi: 10.3934/dcds.2014.34.2405 
[18] 
Felicia Maria G. Magpantay, Xingfu Zou. Wave fronts in neuronal fields with nonlocal postsynaptic axonal connections and delayed nonlocal feedback connections. Mathematical Biosciences & Engineering, 2010, 7 (2) : 421442. doi: 10.3934/mbe.2010.7.421 
[19] 
Lijun Zhang, Yixia Shi, Maoan Han. Smooth and singular traveling wave solutions for the SerreGreenNaghdi equations. Discrete & Continuous Dynamical Systems  S, 2020, 13 (10) : 29172926. doi: 10.3934/dcdss.2020217 
[20] 
Hongqiu Chen, Jerry L. Bona. Periodic travelingwave solutions of nonlinear dispersive evolution equations. Discrete & Continuous Dynamical Systems  A, 2013, 33 (11&12) : 48414873. doi: 10.3934/dcds.2013.33.4841 
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