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  1. Article

    Open Access

    Distributed Nonlocal Feedback Delays May Destabilize Fronts in Neural Fields, Distributed Transmission Delays Do Not

    The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural fi...

    Axel Hutt, Linghai Zhang in The Journal of Mathematical Neuroscience (2013)

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    Article

    Explicit traveling wave solutions to nonlinear evolution equations

    First of all, some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations, nonlinear dissipative dispersive wave equations, nonlinear co...

    Linghai Zhang in Chinese Annals of Mathematics, Series B (2011)

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    Article

    Speeds of traveling waves in some integro-differential equations arising from neuronal networks

    We study traveling waves of some integro-differential equations arising from synaptically coupled neuronal networks. We investigate the influence of synaptic couplings and parameter values on the propagation o...

    Eiji Yanagida, Linghai Zhang in Japan Journal of Industrial and Applied Mathematics (2010)

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    Article

    Solutions to some open problems in Fluid dynamics

    Let u = u(x, t, u 0) represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ...

    Linghai Zhang in Chinese Annals of Mathematics, Series B (2008)

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    Article

    Dynamics of neuronal waves

    First of all, by studying the existence and stability of traveling wave fronts of the following nonlinear nonlocal model equation $$u_t+au_x+u=\alpha\mathop{\int}_{\mathbb R}K(x-y)H(u(y,t)-\the...

    Linghai Zhang in Mathematische Zeitschrift (2007)

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    Article

    Traveling Waves of a Singularly Perturbed System of Integral–Differential Equations Arising from Neuronal Networks

    A nonlinear nonlocal model arising from synaptically coupled neuronal networks with two integral terms is considered. The existence and stability of several traveling wave solutions are established by using id...

    Linghai Zhang in Journal of Dynamics and Differential Equations (2005)

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    Article

    Exponential Stability of Traveling Pulse Solutions of a Singularly Perturbed System of Integral Differential Equations Arising From Excitatory Neuronal Networks

    We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly perturbed systems of integral di.erential equations arising from neuronal networks. It has been proved that expo...

    Linghai Zhang in Acta Mathematicae Applicatae Sinica, English Series (2004)

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    Article

    Dissipation and Decay Estimates

    We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any futu...

    Linghai Zhang in Acta Mathematicae Applicatae Sinica (2004)

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    Article

    Decay of global solutions of two nonlinear evolution equations

    We study the decay of solutions of two nonlinear evolution equations: the Benjamin-Ono-Burgers and the Schrodinger-Burgers equations. We establish sharp rates ofL 2 decay of global solutions to these problems, wi...

    Boling Guo, Linghai Zhang in Acta Mathematicae Applicatae Sinica (1997)

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    Article

    Asymptotic property for the solution to the generalized Korteweg-de vries equation

    We study temporal asymptotic property for the solution of the initial value problem for the generalized nonlinear Korteweg-de Vries equation, which is a nonlinear dissipative dispersive wave equation. The deca...

    Linghai Zhang in Acta Mathematicae Applicatae Sinica (1994)

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    Article

    Initial value problem for a nonlinear parabolic equation with singular integral-differential term

    We study the initial value problem for a nonlinear parabolic equation with singular integral-differential term. By means of a series of a priori estimations of the solutions to the problem and Leray-Schauder f...

    Linghai Zhang in Acta Mathematicae Applicatae Sinica (1992)