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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 and Continuous Dynamical Systems, 2009, 24 (3) : 659-673. 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 and Continuous Dynamical Systems - B, 2017, 22 (7) : 3007-3022. doi: 10.3934/dcdsb.2017160 |
[3] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[4] |
Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1507-1522. doi: 10.3934/dcdsb.2014.19.1507 |
[5] |
Min He. A class of integrodifferential equations and applications. Conference Publications, 2005, 2005 (Special) : 386-396. 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 and Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 |
[7] |
Aijun Zhang. Traveling wave solutions of periodic nonlocal Fisher-KPP equations with non-compact asymmetric kernel. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022061 |
[8] |
Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang. Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1331-1353. doi: 10.3934/dcds.2016.36.1331 |
[9] |
Yicheng Jiang, Kaijun Zhang. Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations. Kinetic and Related Models, 2018, 11 (5) : 1235-1253. doi: 10.3934/krm.2018048 |
[10] |
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) : 11-24. doi: 10.3934/mfc.2020002 |
[11] |
Guangying Lv, Mingxin Wang. Existence, uniqueness and stability of traveling wave fronts of discrete quasi-linear equations with delay. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 415-433. doi: 10.3934/dcdsb.2010.13.415 |
[12] |
Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681 |
[13] |
Stephan Didas, Joachim Weickert. Integrodifferential equations for continuous multiscale wavelet shrinkage. Inverse Problems and Imaging, 2007, 1 (1) : 47-62. doi: 10.3934/ipi.2007.1.47 |
[14] |
Paola Loreti, Daniela Sforza. Inverse observability inequalities for integrodifferential equations in square domains. Evolution Equations and Control Theory, 2018, 7 (1) : 61-77. doi: 10.3934/eect.2018004 |
[15] |
Mathias Nikolai Arnesen. Existence of solitary-wave solutions to nonlocal equations. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3483-3510. doi: 10.3934/dcds.2016.36.3483 |
[16] |
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 |
[17] |
Weiran Sun, Min Tang. A relaxation method for one dimensional traveling waves of singular and nonlocal equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1459-1491. doi: 10.3934/dcdsb.2013.18.1459 |
[18] |
Albert Erkip, Abba I. Ramadan. Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2125-2132. doi: 10.3934/cpaa.2017105 |
[19] |
Linghai Zhang. Wave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networks. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2405-2450. doi: 10.3934/dcds.2014.34.2405 |
[20] |
Felicia Maria G. Magpantay, Xingfu Zou. Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback connections. Mathematical Biosciences & Engineering, 2010, 7 (2) : 421-442. doi: 10.3934/mbe.2010.7.421 |
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