Minling Zheng

• PhD
• Huzhou University

Urban flood risk management has been a hot issue worldwide due to the increased frequency and severity of floods occurring in cities. In this paper, an innovative modelling approach based on the Bayesian convolutional neural network (BCNN) was proposed to simulate the urban flood inundation, and to provide a reliable prediction of specific water de...

We prove a new existence result for the Fokker-Planck-Boltzmann equation with an initial data with infinite energy in the framework of renormalization. We extend the result of DiPerna-Lions.

It is often challenging to selectively segment the images with intensity inhomogeneity for the existing region-based variational models. This article proposes a Retinex-based selective segmentation model for inhomogeneous images. The main idea is to employ the Retinex theory to decouple the input inhomogeneous image into illumination bias and refle...

In this paper, we propose an adaptive total generalized variation model for removing the speckle noise in ultrasound image. The existence and uniqueness of the minimizers to the proposed model are established. Furthermore, we design an alternating minimization algorithm to solve numerically the model. By incorporating the generalized cross validati...

This chapter is concerned with fractional dynamical systems which occur in many engineering and scientific research fields. The chapter presents an unstructured-mesh Galerkin finite element method for solving the 2D multiterm time-space fractional Bloch–Torrey equations, a finite difference/finite element method for a 2D multiterm time-fractional m...

This chapter is concerned with fractional dynamic systems which occur in many engineering and scientific research fields. These include a variety of multiterm time/time-space fractional dynamic systems. The chapter presents the analytical solution for the multiterm time-fractional model; the fractional predictor-corrector method for the multiterm t...

The fractional Laplacian, (−△)s, s∈(0,1), appears in a wide range of physical systems, including Lévy flights, some stochastic interfaces, and theoretical physics in connection to the problem of stability of the matter. In this paper, a matrix transfer technique (MTT) is employed combining with spectral/element method to solve fractional diffusion...

In this work, we studied the radial point interpolation collocation method (RIPCM) for the solution of the partial differential models with fractional derivatives. In the present meshless method, polynomial basis function and two novel types local support fields were considered. The (time-)space fractional differential equations with single-term or...

The purpose of this paper is to investigate a high order numerical method for solving time-fractional Black-Scholes equation in which the fractional operator is defined by the Caputo fractional derivative. The proposed space-time spectral method employs the Jacobi polynomials for the temporal discretisation and Fourier-like basis functions for the...

In this paper, a spectral collocation method is proposed and analyzed for solving the time fractional Schrödinger equation. The space derivative is discretized using the collocation method and the time fractional derivative using Grünwald–Letnikov formulation. The stability and convergence of the full discretization scheme are analyzed based on the...

Color transfer methods usually suffer from spatial color coherency problem. In order to address this problem, this paper develops a fused color transfer method for image colorization. Our idea is to design a local student's t-test to screen the incoherent colors in the preliminary colorization results obtained by a simple color transfer method with...

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergen...

The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex systems. This paper aims to develop a high order numerical method for solving multi-term time-fractional diffusion equations. Based on the space-time spectral method, a high-order scheme is proposed in the present paper. In this method, the Legendre polyno...

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the nonlocal property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presen...

This paper presents a numerical scheme for space fractional diffusion equations (SFDEs) based on pseudo-spectral method. In this approach, using the Guass-Lobatto nodes, the unknown function is approximated by orthogonal polynomials or interpolation polynomials. Then, by using pseudo-spectral method, the SFDE is reduced to a system of ordinary diff...

This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation ∂ tf e{open} + υ·Δ xf e{open} = Q(f e{open},f e{open} + e{open}Δ υf e{open} as e{open} → 0 + We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation inL 1((0,T) × ℝ N × ℝ...

In this paper we study the viscosity analysis of the spatially homogeneous Boltzmann equation for Maxwel-lian molecules. We first show that the global existence in time of the mild solution of the viscosity equation (,) t v f Q f f f          . We then study the asymptotic behaviour of the mild solution as the coefficients 0    , and an...

In this paper, we obtain a lower semicontinuity result with respect to the strong L 1-convergence of the integral functionals $ F(u,\Omega ) = \int\limits_\Omega {f(x,u(x),\varepsilon u(x))dx} $ F(u,\Omega ) = \int\limits_\Omega {f(x,u(x),\varepsilon u(x))dx} defined in the space SBD of special functions with bounded deformation. Here ɛu repre...

We study the existence and uniqueness of the solution to the viscosity equation at ∂ t f=δΔf+Q(f,f) with collision kernel B(|v-v * |,ω)=|v-v * | γ b(cosθ) and δ>0 small enough; especially, we show that the solution f can approach the one of the unperturbed equation in L k 1 -norm while δ goes to 0. Our method mainly relies on the interpolation ineq...