期刊:
Journal of Inequalities and Applications,2021年2021(1):1-15 ISSN:1029-242X
通讯作者:
Wang, Qisheng
作者机构:
[Wang, Keyan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Wang, Qisheng] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Guangdong, Peoples R China.
通讯机构:
[Wang, Qisheng] W;Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Guangdong, Peoples R China.
关键词:
Hyperbolic equation;Expanded mixed finite element method;Two-grid algorithm;Error estimate
摘要:
In this paper, a second-order hyperbolic equation is solved by a two-grid algorithm combined with the expanded mixed finite element method. The error estimate of the expanded mixed finite element method with discrete-time scheme is demonstrated. Moreover, we present a two-grid method and analyze its convergence. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy
$H= \mathcal{O}(h^{\frac{1}{2}})$
. Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method.
摘要:
The Nilaparvata lug ens is primary vector of rice diseases such as rice ragged stunt. A recent study reported the Wolbachia wStri can cause the cytoplasmic incompatibility of N.lugens, and inhibit the infection and transmission of rice ragged stunt virus in the laboratory. In this work, based on multi-strains infection mechanisms including incomplete cytoplasmic incompatibility and imperfect maternal transmission, we use differential equations to describe the spreading dynamics of Wolbachia wStri and wLug in N.lugens population. The system can exhibit one or two stable equilibria. The stability of equilibrium infected with wStri shows that wStri can invade wild populations when the cytoplasmic incompatibility intensity of wStri and the maternal inheritance leakage rate of wLug are higher than some certain thresholds. The stability conditions of the equilibria are related to the mutual fitness of the populations. If one population is more adaptable than the other, it will be in the ascendancy. An initial value region is found, from which the trajectory of system tends to the equilibrium infected with wStri. Studies on subsystem without wStri demonstrate there is a symbiotic relation between Wolbachia wLug and N.lugens population, and Wolbachia wLug can promote the reproduction of N.lugens. In addition, our numerical results are consistent with relevant literatures experimental results. Our results can guide the release of N.lugens infected with wStri in rice fields to control the growth of wild N.lugens population. (C) 2021 Elsevier Ltd. All rights reserved.
摘要:
Motivated by ideas from two-step models and combining second-order TV regularization in the LLT model, we propose a coupling model for MR image reconstruction. By applying the variables splitting technique, the split Bregman iterative scheme, and the alternating minimization method twice, we can divide the proposed model into several subproblems only related to second-order PDEs so as to avoid solving a fourth-order PDE. The solution of every subproblem is based on generalized shrinkage formulas, the shrink operator or the diagonalization technique of the Fourier transform, and hence can be obtained very easily. By means of the Barzilai–Borwein step size selection scheme, an ADMM type algorithm is proposed to solve the equations underlying the proposed model. The results of numerical implementation demonstrate the feasibility and effectiveness of the proposed model and algorithm.
摘要:
The blow-up of solutions of a class of nonlinear viscoelastic Kirchhoff equation with suitable initial data and Dirichlet boundary conditions is discussed. By constructing a suitable auxiliary function to overcome the difficulty of gradient estimation and making use of differential inequality technique, we establish a finite time blow-up result when the initial data is at arbitrary energy level. Moreover, a lower bound of the lifespan is also derived by constructing a control function with both nonlocal term and memory kernel. Compared with the previous literature, our approach to estimate the lifespan does not require the initial energy to control some norms of the solution.
摘要:
In this paper, we investigate the problem for optimal control of a viscous generalized theta-type dispersive equation (VG theta-type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG theta-type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.
作者机构:
[胡立军] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421002, China;[赵昆磊] LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
通讯机构:
[Hu, L.] C;College of Mathematics and Statistics, China
期刊:
Journal of Mathematical Analysis and Applications,2020年488(2):124083- ISSN:0022-247X
通讯作者:
Kovalev, Leonid, V
作者机构:
[Li, Liulan] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Kovalev, Leonid, V] Syracuse Univ, Dept Math, 215 Carnegie, Syracuse, NY 13244 USA.
通讯机构:
[Kovalev, Leonid, V] S;Syracuse Univ, Dept Math, 215 Carnegie, Syracuse, NY 13244 USA.
关键词:
Circle embeddings;Circle homeomorphisms;Blaschke products;Rational functions
摘要:
This paper continues the investigation of the relation between the geometry of a circle embedding and the values of its Fourier coefficients. First, we answer a question of Kovalev and Yang concerning the support of the Fourier transform of a starlike embedding. An important special case of circle embeddings are homeomorphisms of the circle onto itself. Under a one-sided bound on the Fourier support, such homeomorphisms are rational functions related to Blaschke products. We study the structure of rational circle homeomorphisms and show that they form a connected set in the uniform topology. (C) 2020 Elsevier Inc. All rights reserved.
期刊:
Journal of Mathematical Analysis and Applications,2020年486(2):123920- ISSN:0022-247X
通讯作者:
Ponnusamy, Saminathan
作者机构:
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构:
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
摘要:
Let (D) over bar be the closure of the unit disk D in the complex plane C and g be a continuous function in (D) over bar. In this paper, we discuss some characterizations of elliptic mappings f satisfying the Poisson's equation Delta f = g in D, and then establish some sharp distortion theorems on elliptic mappings with the finite perimeter and the finite radial length, respectively. The obtained results are the extension of the corresponding classical results. (C) 2020 Elsevier Inc. All rights reserved.
摘要:
In this paper, we will give new characterizations of Lipschitz-type spaces, and establish related growth theorems for Bloch-type spaces. Then we will present applications to certain PDEs. We will also consider the Dirichlet-type energy integrals and their applications.
摘要:
When using the conventional direction splitting method to calculate multidimensional high speed gas-dynamical flows, Riemann solvers capable of resolving contact surface and shear wave accurately will suffer from different forms of shock instability, such as the notorious carbuncle phenomenon. The stability analysis shows that the lack of dissipation in the direction transverse to the shock front leads to the shock instability of low-dissipation HLLEM solver. To overcome this defect, an accurate and carbuncle-free genuinely two-dimensional HLL-type Riemann solver is proposed. Using Zha-Bilgen splitting method, the flux vector of two-dimensional Euler equations is split into the convective flux and pressure flux. An algorithm similar to AUSM+ scheme is adopted to calculate the convective flux and the pressure flux is calculated by the low-dissipation HLLEM scheme. Following Balsara's idea, the genuinely two-dimensional properties of the new solver are achieved by solving the two-dimensional Riemann problem that considers transversal features of the flow at each vertex of the cell interface. Numerical results of benchmark tests demonstrate that the new solver has higher resolution and better robustness than the conventional HLLEM solver implemented in dimension by dimension. (C) 2020 Elsevier Ltd. All rights reserved.