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A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS: 《Acta Mathematica Scientia》2024年第5期2019-2040,共22页Li HU Zhiyuan LI Xiaona YANG; supported by National Natural Science Foundation of China(12271277);the Open Research Fund of Key Laboratory of Nonlinear Analysis&Applications(Central China Normal University),Ministry of Education,China.; In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-...; 关键词：fractional diffusion equation inverse source problem nonlocal observation observation UNIQUENESS Tikhonov regularization

THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D: 《Acta Mathematica Scientia》2023年第5期2133-2158,共26页陈亚洲 Hakho HONG 施小丁; partially supported by the NationalNatural Science Foundation of China(12171024,11901025,11971217,11971020);the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027)。; This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard system.This model is usually used to describe the motion of immiscible two-phase flows with a diffusion interface.For the period...; 关键词：Navier-Stokes/Cahn-Hilliard system strong solution existence UNIQUENESS large-time behavior

THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA: 《Acta Mathematica Scientia》2023年第4期1675-1716,共42页王海涛张雄韬; partially the National Key R&D Program of China(2022YFA1007300);the NSFC(11901386,12031013);the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA25010403);the NSFC(11801194,11971188);the Hubei Key Laboratory of Engineering Modeling and Scientific Computing。; A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and ...; 关键词：compressible Navier-Stokes equation BV initial data REGULARITY UNIQUENESS

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS: 《Acta Mathematica Scientia》2023年第3期1131-1160,共30页崔磊磊郭佳星李工宝; supported by the Natural Science Foundation of China(11771166,12071169);the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。; In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critic...; 关键词：Kirchhoff type equations potential functions having non-degenerate critical points the Lyapunov-Schmidt reduction method multi-peak solutions existence and local uniqueness

THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS: 《Acta Mathematica Scientia》2023年第2期469-491,共23页Hakho HONG; The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals ga...; 关键词：Navier-Stokes-Korteweg system van der Waals gas EXISTENCE UNIQUENESS

SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES: 《Acta Mathematica Scientia》2023年第2期821-838,共18页刘曼莉高凌云房少梅; partially supported by the NSFC(11271227,11271161);the PCSIRT(IRT1264);the Fundamental Research Funds of Shandong University(2017JC019)。; In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing sm...; 关键词：meromorphic function in several variables Nevanlinna theory partial differ-ential equation total derivative

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN: 《Acta Mathematica Scientia》2023年第1期450-468,共19页向建立严国政; supported by NSFC(11571132)。; In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.I...; 关键词：conductive boundary condition UNIQUENESS phaseless far field data inverse scattering

THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE: 《Acta Mathematica Scientia》2022年第5期2149-2164,共16页Yujuan CHEN Lei WEI Yimin ZHANG; supported by NSFC(11871250);supported by NSFC(11771127,12171379);the Fundamental Research Funds for the Central Universities(WUT:2020IB011,2020IB017,2020IB019).; We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu)...; 关键词：p-Lapacian Hardy potential SYMMETRY UNIQUENESS asymptotic behavior

THE UNIQUENESS OF THE L_(p) MINKOWSKI PROBLEM FOR q-TORSIONAL RIGIDITY: 《Acta Mathematica Scientia》2021年第5期1405-1416,共12页Guangling SUN Lu XU Ping ZHANG; The authors were supported by NSFC(11771132);Hunan Science and Technology Project(2018JJ1004).; In this paper,we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p>1 and q>1 in smooth case.Meanwhile,the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-tors...; 关键词：q-torsional rigidity L_(p)Minkowski problem L_(p)Hadamard variational formula L_(p)Brunn-Minkowski inequality

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION被引量：2: 《Acta Mathematica Scientia》2021年第3期925-940,共16页Jianli XIANG Guozheng YAN; supported by NSFC(11571132)。; This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pa...; 关键词：Acoustic wave UNIQUENESS mixed reciprocity relation modified interior transmission problem a priori estimates

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