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Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations: 《Acta Mathematicae Applicatae Sinica》2025年第2期414-424,共11页Yu-ting KANG Peng LUO Chang-lin XIANG Xue-xiu ZHONG; partially supported by National Natural Science Foundation of China(Nos.12171183,11831009);the Fundamental Research Funds for the Central Universities(Nos.KJ02072020-0319,CCNU22LJ002);financially supported by National Natural Science Foundation of China(No.12271296);partially supported by National Natural Science Foundation of China(No.11801581);Guangdong Basic and Applied Basic Research Foundation(2021A1515010034);Guangzhou Basic and Applied Basic Research Foundation(202102020225);Province Natural Science Fund of Guangdong(2018A030310082).; In the present paper,we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations-M(∫_(R^(N))|∇_(v)|^(2)dx)Δ^(v)=g(v)in R^(N);where M:[0;+∞)→R is a continuous function satisf...; 关键词：Kirchhoff type equations general nonlinearities UNIQUENESS NONDEGENERACY singular perturbation problem

Traveling Fronts for a Time-periodic Population Model with Dispersal: 《Acta Mathematicae Applicatae Sinica》2024年第4期1147-1154,共8页Hai-qin ZHAO; partially supported by the Natural Science Basic Research Program of Shaanxi(No.2024JCYBMS-025);the Innovation Capability Support Program of Shaanxi(No.2024RS-CXTD-88)。; In this paper,we study a class of time-periodic population model with dispersal.It is well known that the existence of the periodic traveling fronts has been established.However,the uniqueness and stability of such fr...; 关键词：periodic integro-differential equation time-periodic traveling front UNIQUENESS STABILITY

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System: 《Acta Mathematicae Applicatae Sinica》2024年第1期45-74,共30页Ya-zhou Chen Hakho Hong Xiao-ding Shi; supported by the National Natural Science Foundation of China (Nos. 12171024, 11901025,11971217, 11971020);Academic and Technical Leaders Training Plan of Jiangxi Province (No. 20212BCJ23027)。; This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global...; 关键词：Navier-Stokes/Allen-Cahn system EXISTENCE UNIQUENESS large time behavior decay rate

Existence and Regularity of Solution of the Liquid^(4)He Model Coupling with an Applied Magnetic Field: 《Acta Mathematicae Applicatae Sinica》2022年第2期497-511,共15页Chen PENG; supported by the National Natural Science Foundation of China(Nos.11771306,11901408)。; In this paper,we derive a time-dependent Ginzburg-Landau model for liquid^(4)He coupling with an applied magnetic field basing on the Le Chatlier principle.We also obtain the existence and uniqueness of global weak so...; 关键词：Ginzburg-Landau model liquid^(4)He EXISTENCE UNIQUENESS REGULARITY semigroup of operator

Navier-Stokes/Allen-Cahn System with Generalized Navier Boundary Condition: 《Acta Mathematicae Applicatae Sinica》2022年第1期98-115,共18页Ya-zhou CHEN Qiao-lin HE Bin HUANG Xiao-ding SHI; supported by the National Natural Science Foundation of China(Nos.12171024,11901025,11971217,11971020)。; In this paper,we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations.The generalized Navier boundary condition and the r...; 关键词：compressible Navier-Stokes equation Allen-Cahn equation generalized Navier boundary condition EXISTENCE UNIQUENESS

Existence and Properties of Solutions for a Class of Fractional Differential Equations被引量：1: 《Acta Mathematicae Applicatae Sinica》2021年第3期477-484,共8页Yong-qiang XU Shu-hong CHEN Zhong TAN; by the National Natural Science Foundation of China(Nos.11571159,11531010);by the Natural Science Foundation of Fujian Province(Nos.2017J01562).; In this paper,we consider the initial value problem of a class of fractional differential equations.Firstly,we obtain the existence and uniqueness of the solutions by using Picard’s method of successive approximation...; 关键词：EXISTENCE UNIQUENESS fractional derivative equations

Determining a Multi-layered Fluid-solid Medium from the Acoustic Measurements: 《Acta Mathematicae Applicatae Sinica》2020年第1期67-73,共7页Yan-li CUI Feng-long QU; supported by the National Natural Science Foundation of China(Nos.11871416,11771349,91730306);Shandong Provincial Natural Science Foundation(Nos.ZR2019MA027,ZR2017MA044)。; Consider the inverse problem of recovering a multi-layered fluid-solid medium from many acoustic measurements corresponding to time-harmonic acoustic plane waves.We prove that both the supports of the embedded solid o...; 关键词：INVERSE SCATTERING fluid-solid INTERACTION multi-layered MEDIUM UNIQUENESS

Uniqueness to Some Inverse Source Problems for the Wave Equation in Unbounded Domains: 《Acta Mathematicae Applicatae Sinica》2020年第1期134-150,共17页Guang-hui HU Yavar KIAN Yue ZHAO; supported by the National Natural Science Foundation of China(No.11671028);the NSAF grant(No.U1930402)in the National Natural Science Foundation of China;supported by the French National Research Agency ANR(project MultiOnde)grant ANR-17-CE40-0029。; This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind.The measurement data are taken at a surface far away from the source support....; 关键词：INVERSE SOURCE problems LAPLACE transform moving point SOURCE UNIQUENESS

Observability Inequality for the Petrovsky Equation: 《Acta Mathematicae Applicatae Sinica》2016年第3期771-780,共10页Zhong-yu BAI Shu-gen CHAI; Supported by the Natural Science Foundation of Hainan Province(No.20161011); The aim of this paper is to study the exact controllability of the Petrovsky equation. Under some checkable geometric assumptions, we establish the observability inequality via the multiplier method for the Dirichlet ...; 关键词：exact controllability compact uniqueness multiplier method

Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations被引量：1: 《Acta Mathematicae Applicatae Sinica》2016年第1期1-16,共16页Quan-sen JIU Huan YU; supported by National Natural Sciences Foundation of China(No.11171229,11231006 and 11228102);project of Beijing Chang Chen Xue Zhe; In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the he...; 关键词：generalized Navier-Stokes-Boussinesq equations global well-posedness uniqueness fourier localization

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