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数学物理学报（英文版）
数学物理学报（英文版）

丁夏畦 王世全

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0252-9602

actams@wipm.ac.cn

027-87199206

430071

武昌小洪山（武汉市71010信箱）

数学物理学报（英文版）/Journal Acta Mathematica ScientiaCSCDCSTPCDSCI
查看更多>>本刊是我国数学物理学界委托中国科学院武汉物理与数学研究所主办的，以刊登数学与物理科学的边缘学科中具有创造性的代表学科水平的科研成果为主的综合性学术刊物。读者对象是国内外本学科范围的科技工作者。
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    THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

    肖存涛邱华姚正安
    973-983页
    查看更多>>摘要：In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.
      原文链接:
    • 万方数据
    • 维普

    MINIMIZERS OF L2-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

    陈彬高永帅郭玉劲吴越...
    984-996页
    查看更多>>摘要：This paper is concerned with the minimizers of L2-subcritical constraint varia-tional problems with spatially decaying nonlinearities in a bounded domain Ω of RN(N ≥ 1).We prove that the problem admits minimizers for any M＞0.Moreover,the limiting behavior of minimizers as M → oo is also analyzed rigorously.
      原文链接:
    • 万方数据

    MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE FRACTIONAL SCHRODINGER-POISSON SYSTEM WITH DOUBLY CRITICAL GROWTH

    孟禹希贺小明
    997-1019页
    查看更多>>摘要：In this paper,we are concerned with solutions to the fractional Schrödinger-Poisson system{(-Δ)su-φ|u|2*s-3u=λu+μ|u|q-2u+|u|2*s-2u,x ∈ R3,(-Δ)sφ=|u|2*s-1,x ∈ R3,with prescribed mass ∫R3|u|2dx=a2,where a＞0 is a prescribed number,p＞0 is a paremeter,s ∈(0,1),2＜q＜2*,and 2*=362is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L2-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrödinger-Poisson system with a nonlocal critical term.
      原文链接:
    • 万方数据

    THE RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR PROBLEMS INVOLVING WEIGHTED FRACTIONAL LAPLACIANS

    王英邱妍静尹青苹
    1020-1035页
    查看更多>>摘要：This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)sγu=b(x)f(u)in B1 \ {0},u=h in RN\B1,where b:B1→ R is locally Hölder continuous,radially symmetric and decreasing in the|x|direction,f:R → R is a Lipschitz function,h:B1 → R is radially symmetric,decreasing with respect to|x|in RN \ B1,B1 is the unit ball centered at the origin,and(-Δ)sγ is the weighted fractional Laplacian with s ∈(0,1),γ ∈[0,2s)defined by(-Δ)sγu(x)=cN,s limδ→0+∫RN\Bδ(x)u(x)-u(y)/|x-y|N+2s|y|γdy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal prob-lem in whole space(-Δ)sγu(x)=b(x)f(u)in RN \ {0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)su+μ/|x|2su=b(x)f(u)in B1 \ {0},u=h in RN\B1,under suitable additional assumptions on b,f and h.
      原文链接:
    • 万方数据
    • 维普

    THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

    许兰喜关芳芳
    1036-1045页
    查看更多>>摘要：The nonlinear stability of plane parallel shear flows with respect to tilted per-turbations is studied by energy methods.Tilted perturbation refers to the fact that per-turbations form an angle θ ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.
      原文链接:
    • 万方数据
    • 维普

    DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

    涂馨予穆春来邱蜀燕张静...
    1046-1063页
    查看更多>>摘要：In this paper,we consider the fully parabolic chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μukx ∈Ω,t＞0,vt=Δv+wz,x ∈Ω,t＞0,wt=-wz,x ∈ Ω,t＞0,zt=Δz-z+u,x ∈ Ω,t＞0,where Ω ⊂ Rn(n ≥ 1)is a smooth and bounded domain,λ ≥ 0,μ ≥ 0,κ＞1,and the motility function satisfies that γ(v)∈ C3([0,oo)),γ(v)＞0,γ'(v)＜0 for all v ≥ 0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the fol-lowing conditions holds:(ⅰ)λ=μ=0,1 ≤ n ≤ 3;(ⅱ)λ＞0,μ＞0,combined with κ＞1,1 ≤n ≤ 3 or k＞n+2/4,n＞3.Moreover,we prove that the solution(u,v,w,z)exponentially converges to the constant steady state((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).
      原文链接:
    • 万方数据
    • 维普

    THE OPTIMAL LARGE TIME BEHAVIOR OF 3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

    王涵张映辉
    1064-1095页
    查看更多>>摘要：We are concerned with the large-time behavior of 3D quasilinear hyperbolic e-quations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L2 convergence rate of the k(e[0,3])-order spatial derivatives of the solution is(1+t)-3+2k/4.Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
      原文链接:
    • 万方数据

    THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

    赵敏袁荣
    1096-1114页
    查看更多>>摘要：In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.
      原文链接:
    • 万方数据
    • 维普

    THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

    杨纪华
    1115-1144页
    查看更多>>摘要：This paper deals with the problem of limit cycles for the whirling pendulum equation(x)=y,(y)=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.
      原文链接:
    • 万方数据
    • 维普

    A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

    冯立超张春艳曹进德武志辉...
    1145-1164页
    查看更多>>摘要：Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS)under a highly nonlinear constraint in the H∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii func-tionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H∞ and exponential forms,but also the polynomial form and even a general form.
      原文链接:
    • 万方数据
    • 维普