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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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 ...
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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...
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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...
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Article
Open AccessDistributed 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...