数学物理学报(英文版)

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THE RELATIVE VOLUME FUNCTION AND THE CAPACITY OF SPHERE ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS

Xiaoshang JIN

数学物理学报(英文版). 2025 (3): 755-770. DOI: 10.1007/s10473-025-0301-9

摘要 ( 34 )

Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the regularity of this function. We use this function to provide an accurate characterization of the height of the geodesic defining function for the AH manifold with a given boundary metric. Furthermore, it is shown that such functions are uniformly bounded from below at infinity and the bound only depends on the dimension. In the end, we apply this function to study the capacity of balls in AH manifolds and demonstrate that the "relative $p$-capacity function" coincides with the relative volume function under appropriate curvature conditions.

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COMMUTATOR ESTIMATES FOR VECTOR FIELDS ON BESOV SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY

BenMahmoud SALAH

数学物理学报(英文版). 2025 (3): 771-788. DOI: 10.1007/s10473-025-0302-8

摘要 ( 18 )

In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability, and under no vanishing assumptions on the divergence of vector fields. Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fluid mechanics.

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AN EXTENSION OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

Huoxiong WU, Lin WU

数学物理学报(英文版). 2025 (3): 789-808. DOI: 10.1007/s10473-025-0303-7

摘要 ( 20 )

This paper considers the following Marcinkiewicz type integrals $$\mu_{\Omega,\beta }f(x) = \left ( \int_{0}^{\infty } \left | \int_{| x-y |\le t }^{} \frac{\Omega (x-y)}{| x-y|^{n-1-\beta }} f(y){\rm d}y \right | ^{2}\frac{{\rm d}t}{t^3} \right )^{{1}/{2} },\quad 0<\beta<n,$$ which can be regarded as an extension of the classical Marcinkiewicz integral $\mu_\Omega$ introduced by Stein in [Trans Amer Math Soc, 88(1958): 159-172], where $\Omega$ is a homogeneous function of degree zero on $\mathbb{R}^n$ with mean value zero in the unit sphere $S^{n-1}$. Under the assumption that $\Omega\in L^{\infty}(S^{n-1})$, the authors establish the $L^q$-estimate and weak $(1,1)$ type estimate as well as the corresponding weighted estimates for $\mu_{\Omega,\beta}$ with $1<q<\infty$ and $0<\beta<{(q-1)n}/{q}$. Moreover, the bounds do not depend on $\beta$ and the strong $(q,q)$ type and weak $(1,1)$ type estimates for the classical Marcinkiewicz integral $\mu_{\Omega}$ can be recovered from the above estimates of $\mu_{\Omega,\beta}$ when $\beta\to 0$.

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COMPACT LINEAR COMBINATIONS OF COMPOSITION OPERATORS ON THE UNIT BALL

Chunyu DONG, Xin GUO, Qijian KANG

数学物理学报(英文版). 2025 (3): 809-824. DOI: 10.1007/s10473-025-0304-6

摘要 ( 18 )

Recently, Choe-Koo-Wang (J Funct Anal, 2020, 278: 108393) demonstrated the rigid phenomenon: The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC), implies that each difference is compact on the weighted Bergman space in the unit disk. Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces, Korenblum spaces and bounded holomorphic function spaces, we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball. Furthermore, we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition (CNC) on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.

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CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

Zhiyuan FU, Heju YANG, Na XU

数学物理学报(英文版). 2025 (3): 825-836. DOI: 10.1007/s10473-025-0305-5

摘要 ( 14 )

Firstly, the definition of $k$-monogenic function with $\alpha$-weight in superspace is given and a series of properties of this function are discussed. Then the Cauchy-Pompeiu formula for $k$-monogenic function with $\alpha$-weight is obtained. Lastly, the Cauchy integral theorem for $k$-monogenic function with $\alpha$-weight is proved.

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DETECTING THE SLOWLY GROWING SOLUTIONS OF SECOND ORDER LINEAR DIFFERENCE EQUATIONS

Zongxuan CHEN, Zhibo HUANG, Jun WANG, Xiumin ZHENG

数学物理学报(英文版). 2025 (3): 837-854. DOI: 10.1007/s10473-025-0306-4

摘要 ( 13 )

By using asymptotic method, we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara's Wiman-Valiron method and Ishizaki-Wen's binomial series method. The classical problem on finding conditions on the polynomial coefficients $P_{j}(z) ~(j=0,1,2)$ and $F(z)$ to guarantee that all nontrivial solutions of complex second order difference equation $ P_2(z)f(z+2)+P_1(z)f(z+1)+P_0(z)f(z)=F(z)$ has slowly growing solutions with order $1/2$ is detected.

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FUNCTIONAL INEQUALITIES, ISOMORPHISMS AND DERIVATIONS ON BANACH ALGEBRAS

Hamid KHODAEI

数学物理学报(英文版). 2025 (3): 855-866. DOI: 10.1007/s10473-025-0307-3

摘要 ( 13 )

We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables. Applications in connection with asymptotic behaviors of isomorphisms, derivations and $n$-Jordan derivations on Banach algebras are also provided. The results of this paper correct and improve the main results of [12, 16, 22, 23] and improve the corresponding results in [2, 9, 27], but under weaker assumptions.

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THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

Ni XIANG, Yuni XIONG, Jingyi YAO

数学物理学报(英文版). 2025 (3): 867-884. DOI: 10.1007/s10473-025-0308-2

摘要 ( 10 )

In this paper, we derive the a priori estimates for a class of more general $(k,l)$-Hessian quotient type equations involving $u$ and $Du$ on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the $k$-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.

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MULTIPLICITY AND CONCENTRATION OF SOLUTIONS TO A FRACTIONAL $\frac{N}{S}$-LAPLACIAN PROBLEM WITH EXPONENTIAL CRITICAL GROWTH AND POTENTIALS COMPETITION

Wei CHEN, Chao JI, Nguyen Van THIN

数学物理学报(英文版). 2025 (3): 885-918. DOI: 10.1007/s10473-025-0309-1

摘要 ( 10 )

By using the Ljusternik-Schnirelmann category and variational method, we study the existence, multiplicity and concentration of solutions to the fractional Schrödinger equation with potentials competition as follows, $$ \varepsilon^{N}(-\Delta)_{N/s}^{s}u+V(x)|u|^{\frac{N}{s}-2}u=Q(x)h(u)\,\,in\,\, \mathbb R^{N},$$ where $\varepsilon>0$ is a parameter, $s\in (0,1)$, $2\le p<+\infty$ and $N=ps$. The nonlinear term $h$ is a differentiable function with exponential critical growth, the absorption potential $V$ and the reaction potential $Q$ are continuous functions.

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GLOBAL CLASSICAL SOLUTIONS OF 3D COMPRESSIBLE MICROPOLAR FLUIDS WITH FAR-FIELD VACUUM

Mingyu ZHANG

数学物理学报(英文版). 2025 (3): 919-936. DOI: 10.1007/s10473-025-0310-8

摘要 ( 11 )

This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space $\mathbb{R}^3$. For regular initial data with $m_0E_0$ is suitable small, where $m_0$ and $E_0$ represent the upper bound of initial density and initial energy, we prove that if $\rho_0\in L^{\gamma}\cap H^3$ with $\gamma \in (1, 6)$, then the problem possesses a unique global classical solution on $\mathbb{R}^3 \times [0, T]$ with any $T\in (0, \infty)$. It's worth noting that both the vacuum states and possible random largeness of initial energy are allowed.

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ON SINGULARITY FORMATION FOR 3-$D$ ZERO PRESSURE FLOW

Wei HUO

数学物理学报(英文版). 2025 (3): 937-950. DOI: 10.1007/s10473-025-0311-7

摘要 ( 7 )

We provide the breakdown mechanism of pressureless gases when the initial vorticity is zero. In other words, the maximum norm of the divergence and $\Vert u\Vert_{H^{\frac{1}{2}}}$ control the breakdown of the solution. Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.

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GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

Qingyan LI, Zhenhua GUO

数学物理学报(英文版). 2025 (3): 951-981. DOI: 10.1007/s10473-025-0312-6

摘要 ( 9 )

In this paper, we consider an initial boundary value problem for the nonhomogeneous heat-conducting magnetohydrodynamic fluids when the viscosity $\mu$, magnetic diffusivity $\nu$ and heat conductivity $\kappa$ depend on the temperature $\theta$ according to $\mu(\theta)=\theta^{\alpha}$, $\ \kappa(\theta)=\theta^{\beta}$, $\nu(\theta)=\theta^{\gamma}$, with $\alpha$, $\gamma>0$, $\beta\geq 0$. We prove the global existence of a unique strong solution provided that $\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|H_0\|_{L^2}^2+\beta\|\sqrt{\rho_0}\theta_0\|_{L^2}^2$ is suitably small. In addition, we also get some results of the large-time behavior and exponential decay estimates.

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GLOBAL DYNAMICS OF A SPATIAL SOLOW-SWAN MODEL WITH DENSITY-DEPENDENT MOTION

Songzhi LI, Changchun LIU, Ming MEI

数学物理学报(英文版). 2025 (3): 982-1004. DOI: 10.1007/s10473-025-0313-5

摘要 ( 12 )

In this paper, we consider the following spatial Solow-Swan model with density-dependent motion $$\begin{align*} \left\{ \begin{aligned} &u_t=\Delta(\phi(v)u)+\mu u(1-u^\sigma), \quad &x&\in\Omega, t>0, \\ &v_t=\Delta v-v+u^{1-\alpha}v^\alpha, &x&\in\Omega, t>0, \\ &\frac{\partial u}{\partial \nu}=\frac{\partial v}{\partial \nu}=0, &x&\in\partial\Omega, t>0, \\ &u(x,0)=u_0(x), v(x,0)=v_0(x), &x&\in \Omega, \end{aligned} \right. \end{align*}$$ where $ \sigma>0, \alpha\in(0,1) $ and $ \Omega\subset \mathbb{R}^n $ $ (n\ge1) $ is a bounded domain with smooth boundary and $ \phi\in C^3([0,\infty)), \phi(s)>0 \text{ for all } s\ge0 $. We prove that if $$\begin{align*} \left\{ \begin{aligned} & \sigma+\alpha>\max\{1,\frac n2(1-\alpha)\}, &\text{ for }&\mu>0, \\ & 1-\alpha< \frac2n, &\text{ for }& \mu=0, \end{aligned} \right. \end{align*}$$ then there exists a unique time-globally classical solution $(u,v)$ for all $n\ge1$, such a solution is bounded and satisfies $u\ge0$, $v>0$. Moreover, we show that the above solution will convergence to the steady state $(1,1)$ exponentially in $L^\infty$ as $t\to\infty$.

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SPREADING SPEED FOR A TIME-SPACE PERIODIC EPIDEMIC MODEL IN DISCRETE MEDIA

Haiqin ZHAO

数学物理学报(英文版). 2025 (3): 1005-1018. DOI: 10.1007/s10473-025-0314-4

摘要 ( 10 )

This paper is devoted to investigating the spreading speed of a time-space periodic epidemic model with vital dynamics and standard incidence in discrete media. We establish the existence of the leftward and rightward spreading speeds for the infective individuals, which can be used to estimate how fast the disease spreads. To overcome the difficulty arising from the lack of comparison principle for such time-space periodic non-monotone systems, our proof is mainly based on constructing a series of scalar time-space periodic equations, establishing the spreading speeds for such auxiliary equations and using comparison methods. It may be the first work to study the spreading speed for time-space periodic non-monotone systems.

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STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

Zhigang WU, Fuyi XU

数学物理学报(英文版). 2025 (3): 1019-1044. DOI: 10.1007/s10473-025-0315-3

摘要 ( 10 )

The present paper deals with the Cauchy problem to a two-fluid plasma model with unequal viscosities in any dimension $N\geq2$. Employing the precise spectral analysis for the corresponding linearized system, we prove the global well-posedness provided that the initial data are close to a stable equilibrium state in critical functional framework which is not related to the energy space. Moreover, the optimal decay rates for the constructed global solution are also established.

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GLOBAL STRONG SOLUTION OF THE PRESSURELESS NAVIER-STOKES/NAVIER-STOKES SYSTEM

Yue ZHANG, Minyan YU, Houzhi TANG

数学物理学报(英文版). 2025 (3): 1045-1062. DOI: 10.1007/s10473-025-0316-2

摘要 ( 14 )

We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system, which consists of the pressureless Navier-Stokes equations for $(n,w)$ coupled with the isentropic compressible Navier-Stokes equations for $(\rho,u)$ through a drag force term $n(w-u)$. We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state. However, due to the pressureless structure, one can only deal with the density $n$ of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity $w$ of the pressureless flow. To this end, we make use of the spectral analysis, low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of $(w,\rho,u)$ and consequently establish the Lyapunov stability of the density $n$ in Sobolev space.

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SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

Zhen QIU, Guangwu WANG

数学物理学报(英文版). 2025 (3): 1063-1077. DOI: 10.1007/s10473-025-0317-1

摘要 ( 10 )

In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500-2516].

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ASYMPTOTICS OF LARGE DEVIATIONS OF FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION

Diancong JIN, Derui SHENG

数学物理学报(英文版). 2025 (3): 1078-1106. DOI: 10.1007/s10473-025-0318-0

摘要 ( 10 )

In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn-Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the $\Gamma$-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the $\Gamma$-convergence of objective functions.

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REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

Ziling CHENG, Zenghu LI

数学物理学报(英文版). 2025 (3): 1107-1136. DOI: 10.1007/s10473-025-0319-z

摘要 ( 9 )

We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.

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ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF THE INTEGRAL SYSTEM INVOLVING $M$ EQUATIONS

Ling LI

数学物理学报(英文版). 2025 (3): 1137-1154. DOI: 10.1007/s10473-025-0320-6

摘要 ( 11 )

In this paper, we study an integral system involving $m$ equations $$\left\{ \begin{aligned} u_i(x) &= \int_{\mathbb{R}^n}\frac{u_{i+1}^{p_{i+1}}(y)}{|x-y|^{n-\alpha}}{\rm d}y, \quad i=1,2,\cdots,m-1, \\ u_m(x) &= \int_{\mathbb{R}^n}\frac{u_{1}^{p_{1}}(y)}{|x-y|^{n-\alpha}}{\rm d}y, \quad m\geq3,\ n\geq1, \end{aligned} \right. $$ where $u_i>0$ in $\mathbb{R}^n$, $0<\alpha<n$, and $p_i>1 \ (i=1,2,\cdots,m).$ Based on the optimal integrability intervals, we estimate the decay rates of the positive solutions of the system at infinity. But estimating these rates is difficult because the relation between $p_i \ (i=1,2,\cdots,m)$ is uncertain. To overcome this difficulty, we obtain the asymptotic behavior of all cases by discussing them separately. In addition, we also get the radial symmetry of positive solutions under some integrability condition.

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MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS WITH $K$ EXPONENTIAL TERMS

Minfeng CHEN, Meili LIANG, Zongsheng GAO

数学物理学报(英文版). 2025 (3): 1155-1168. DOI: 10.1007/s10473-025-0321-5

摘要 ( 11 )

In this article,~we study the meromorphic solutions of the following non-linear differential equation $\begin{equation*} f^{n}(z)+P_{d}(z,f)=\sum_{j=1}^{k}p_{j}{\rm e}^{\alpha_{j}z}, \end{equation*}$ where $n$ and $k$ are integers with $n\geq k\geq 3$, $P_{d}(z,f)$ is a differential polynomial in $f$ of degree $d\leq n-1$, $p_{j}'s$ and $\alpha_{j}'s$ are non-zero constants. We obtain the expressions of meromorphic solutions of the above equations under some restrictions on $\alpha_{j}'s$. Some examples are given to illustrate the possibilities of our results.

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HOPF BIFURCATION PROBLEM BY PERTURBING A CLASS OF QUARTIC LINEAR-LIKE HAMILTONIAN SYSTEMS

Yanqin XIONG, Guangping HU

数学物理学报(英文版). 2025 (3): 1169-1187. DOI: 10.1007/s10473-025-0322-4

摘要 ( 7 )

We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.

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PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

Ziwei WANG, Lin SUN, Fanchao KONG, Rathinasamy SAKTHIVEL

数学物理学报(英文版). 2025 (3): 1188-1204. DOI: 10.1007/s10473-025-0323-3

摘要 ( 6 )

In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.

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MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

Hongwu ZHANG, Yanhui LI

数学物理学报(英文版). 2025 (3): 1205-1222. DOI: 10.1007/s10473-025-0324-2

摘要 ( 11 )

In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.

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MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT METHODS FOR SOLVING A SUPPLY CHAIN NETWORK EQUILIBRIUM MODEL

Zhuang SHAN

数学物理学报(英文版). 2025 (3): 1223-1234. DOI: 10.1007/s10473-025-0325-1

摘要 ( 7 )

Using a modified subgradient extragradient algorithm, this paper proposed a novel approach to solving a supply chain network equilibrium model. The method extends the scope of optimisation and improves the accuracy at each iteration by incorporating adaptive parameter selection and a more general subgradient projection operator. The advantages of the proposed method are highlighted by the proof of strong convergence presented in the paper. Several concrete examples are given to demonstrate the effectiveness of the algorithm, with comparisons illustrating its superior CPU running time compared to alternative techniques. The practical applicability of the algorithm is also demonstrated by applying it to a realistic supply chain network model.

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