15 papers
Analysis and approximation for inverse potential problem of space-dependent variable-exponent sub-diffusion in heterogeneous medium
Zhiyuan Li, Chunlong Sun, Xiangcheng Zheng
Anomalous transport in complex heterogeneous medium is often characterized by non-Markovian memory effects and spatially varying trapping properties. From the point of view of cont…
High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel
Wenlin Qiu, Chuanwei Su, Xiangcheng Zheng
We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the s…
Analysis and Approximation of Stochastic Multiscale Subdiffusion Driven by Fractional Gaussian Noise
Jincheng Dong, Ning Du, Xu Guo +2
This paper investigates a stochastic multiscale subdiffusion model driven by fractional Gaussian noise, where the multiscale Abel kernel with variable exponent is us…
Multiscale solution decomposition of nonlocal-in-time problems with application in numerical computation
Mengmeng Liu, Jie Ma, Wenlin Qiu +1
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original…
Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
Yingwen Guo, Yinnian He, Wenlin Qiu +1
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power…
Numerical analysis for subdiffusion problem with non-positive memory
Wenlin Qiu, Xiangcheng Zheng
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such…
Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model
Wenlin Qiu, Xiangcheng Zheng, Tao Guo +1
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is…
Analysis of evolution equation with variable-exponent memory modeling multiscale viscoelasticity
Yiqun Li, Xiangcheng Zheng
We investigate the well-posedness and solution regularity of an evolution equation with non-positive type variable-exponent memory, which describes multiscale viscoelasticity in ma…
Inverse source problem of sub-diffusion of variable exponent
Zhiyuan Li, Chunlong Sun, Xiangcheng Zheng
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theore…
Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping
Wenlin Qiu, Xiangcheng Zheng, Kassem Mustapha
This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal dampin…
A multiscale Abel kernel and application in viscoelastic problem
Wenlin Qiu, Tao Guo, Yiqun Li +2
We consider the variable-exponent Abel kernel and demonstrate its multiscale nature in modeling crossover dynamics from the initial quasi-exponential behavior to long-term power-la…
Generalizing subdiffusive Black-Scholes model by variable exponent: Model transformation and numerical approximation
Meihui Zhang, Yaxue Liu, Mengmeng Liu +2
This work generalizes the subdiffusive Black-Scholes model by introducing the variable exponent in order to provide adequate descriptions for the option pricing, where the variable…
Weighted Sonine conditions and application
Xiangcheng Zheng, Shangqin Zhu, Yiqun Li
The Sonine kernel described by the classical Sonine condition of convolution form is an important class of kernels used in integral equations and nonlocal differential equations. T…
An equivalent formulation of Sonine condition
Xiangcheng Zheng
Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work pro…
Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation
Xiangcheng Zheng, Yiqun Li, Wenlin Qiu
We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model…