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Global weak solutions to a phase-field model for motion of grain boundaries

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Applied Mathematics and Mechanics(English Edition) 2022年第11期43卷 1777-1792页

作者： Zixian ZHU boling guo Shaomei FANG Department of Mathematics Shanghai UniversityShanghai 200444China Institute of Applied Physics and Computational Mathematics Beijing 100088China College of Mathematics and Information South China Agricultural UniversityGuangzhou 510642China

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.

关键词： solid-solid phase transition phase-field model Galerkin method weak solutions

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

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Science China Mathematics 2022年第8期65卷 1553-1576页

作者： Mingjuan Chen boling guo Lijia Han Department of Mathematics Jinan UniversityGuangzhou510632China Institute of Applied Physics and Computational Mathematics Beijing100088China Department of Mathematics and Physics North China Electric Power UniversityBeijing102206China

In this paper,we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_(t)u−ϵ∂^(2)/_(x)u+H∂^(2)_(x)u+uu_(x)=0,where H denotes the Hilbert transform *** obtain that it is uniformly locally well-posed for small data in the refined Sobolev space H~σ(R)(σ■0),which is a subspace of L2(ℝ).It is worth noting that the low-frequency part of H~σ(R)is scaling critical,and thus the small data is *** high-frequency part of H~σ(R)is equal to the Sobolev space Hσ(ℝ)(σ■0)and reduces to L2(ℝ).Furthermore,we also obtain its inviscid limit behavior in H~σ(R)(σ■0).

关键词： Benjamin-Ono-Burgers equation Cauchy problem inviscid limit behavior

Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System

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Numerical Mathematics(Theory,Methods and Applications) 2023年第1期16卷 140-164页

作者： Shasha Bian Yue Cheng boling guo Tingchun Wang The Graduate School of China Academy of Engineering Physics Beijing 100088China School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system,we translate the KGD equations into an equivalent system by introducing an auxiliary function,then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent *** scheme perfectly inherits the mass and energy conservative properties possessed by the KGD,while the energy preserved by the existing conservative numerical schemes expressed by two-level’s solution at each time *** using energy method together with the‘cut-off’function technique,we establish the optimal error estimate of the numerical solution,and the convergence rate is O(τ^(2)+h^(2))in l∞-norm with time stepτand mesh size *** experiments are carried out to support our theoretical conclusions.

关键词： Klein-Gordon-Dirac equation nonlinear finite difference scheme conservation error analysis

Achievements and Contributions in the Field of Partial Differential Equations:Special Issue Dedicated to Academician Zhou Yulin's Centenary Birthday

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偏微分方程:英文版 2023年第2期36卷 119-121页

作者： guo boling Institute of Applied Physics and Computational Mathematics Beijing 100088China

Professor Zhou Yulin was born on February 12,1923 in Shanghai and passed away on March 2,2021 in *** a famous mathematician,he was the deputy director of the Institute of Applied Physics and Computational Mathematics,a member of the Science and Technology Committee of the Chinese Academy of Engineering Physics,and the chairman and honorary chairman of the Chinese Society of Computational Mathematics.

关键词： Academician chairman Yulin

On Local Wellposedness of the Schrodinger-Boussinesq System

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Journal of Partial Differential Equations 2022年第4期35卷 360-381页

作者： SHAO Jjie guo boling Department of Mathematics Nanjing University of Science and TechnologyNanjing210094China Institute of Applied Physics and Computational Mathematics Beijing 100088China The Graduate School of China Academy of Engineering Physics Beijing 100088China

In this paper we prove that the Schrodinger-Boussinesq system with solution(u,v,(-∂xx)-^(2/1)vt)is locally wellposed in H^(s)×H^(s)×Hs^(-1),s≥-1/*** local wellposedness is obtained by the transformation from the problem into a nonlinear Schrodinger type equation system and the contraction mapping theorem in a suitably modified Bourgain type space inspired by the work of Kishimoto,*** result improves the known local wellposedness in H^(s)×H^(s)×H^(s-1),s>-1/4 given by Farah.

关键词： Schrodinger-Boussinesq system Cauchy problem local wellposedness low regularity.

THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM

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Acta Mathematica Scientia 2023年第2期43卷 942-958页

作者：郭柏灵肖亚敏 Institute of Applied Physics and Computational Mathematics Beijing 100088China The Graduate School of China Academy of Engineering Physics Beijing 100088China

This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in *** first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak ***,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).

关键词： global existence propagation regularity KdV system

Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform＊

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Applied Mathematics and Mechanics(English Edition) 2016年第2期37卷 137-150页

作者： Yaqing LIU boling guo Institute of Applied Physics and Computational Mathematics Beijing 100088 China Gengdan Institute of Beijing University of Technology Beijing 101301 China

This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.

关键词： Maxwell fluid fractional derivative radiation heat heat source Laplacetransform

Global solution for quantum Zakharov equations

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Applied Mathematics and Mechanics(English Edition) 2017年第4期38卷 603-616页

作者： Shujun YOU boling guo Department of Mathematics Huaihua University Huaihua 418008 Hunan Province China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

关键词： quantum Zakharov equation initial value problem global solution

Local regularity properties for ID mixed nonlinear Schrodinger equations on half-line

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Frontiers of Mathematics in China 2020年第6期15卷 1121-1142页

作者： boling guo Jun WU Institute of Applied Physics and Computational Mathematics Beijing 100088China Graduate School of China Academy of Engineering Physics Beijing 100088China

The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary *** combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev ***,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.

关键词： Mixed nonlinear Schrodinger(MNLS)equations initial-boundary value problem(IBVP) Bourgain spaces local well-posedness