-
Article
A vector-valued PDE-constrained image inpainting model
In image inpainting, the identification and inpainting of local detail features and the preservation of global features are crucial. Models based on fractional-order partial differential equations exhibit rich...
-
Article
Moiré superlattices in twisted two-dimensional halide perovskites
Moiré superlattices have emerged as a new platform for studying strongly correlated quantum phenomena, but these systems have been largely limited to van der Waals layer two-dimensional materials. Here we intr...
-
Article
Room-temperature epitaxial welding of 3D and 2D perovskites
Formation of epitaxial heterostructures via post-growth self-assembly is important in the design and preparation of functional hybrid systems combining unique properties of the constituents. This is particular...
-
Article
Genetic variations of CAV1 gene contribute to HCC risk: a case–control study
Hepatocellular carcinoma (HCC) is the sixth common cancer and the third common cause of cancer mortality worldwide. However, the exact molecular mechanism of HCC remains uncertain. Caveolin-1 (CAV1) is the mai...
-
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...
-
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...
-
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...
-
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 ...
-
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...
-
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...
-
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...
-
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...
-
Chapter and Conference Paper
A New MOEA for Multi-objective TSP and Its Convergence Property Analysis
Evolutionary Multi-objective Optimization(EMO) is becoming a hot research area and quite a few aspects of Multi-objective Evolutionary algorithms(MOEAs) have been studied and discussed. However there are still...
-
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...
-
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...
-
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...
