数学物理学报(英文版)

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A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION^*

Jinbao Jian, Chen Zhang, Pengjie Liu

数学物理学报(英文版). 2023 (1): 1-24. DOI: 10.1007/s10473-023-0101-z

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This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints. Based on the ideas of splitting and sequential quadratic optimization (SQO), a new feasible descent method for the discussed problem is proposed. First, we consider the problem of quadratic optimal (QO) approximation associated with the current feasible iteration point, and we split the QO into two small-scale QOs which can be solved in parallel. Second, a feasible descent direction for the problem is obtained and a new SQO-type method is proposed, namely, splitting feasible SQO (SF-SQO) method. Moreover, under suitable conditions, we analyse the global convergence, strong convergence and rate of superlinear convergence of the SF-SQO method. Finally, preliminary numerical experiments regarding the economic dispatch of a power system are carried out, and these show that the SF-SQO method is promising.

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GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*

Quansen Jiu, Lin Ma

数学物理学报(英文版). 2023 (1): 25-42. DOI: 10.1007/s10473-023-0102-y

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In this paper, we consider the weak solutions of compressible Navier-Stokes-Landau-Lifshitz-Maxwell (CNSLLM) system for quantum fluids with a linear density dependent viscosity in a 3D torus. By introducing the cold pressure $P_c$, we prove the global existence of weak solutions with the pressure $P+P_c$, where $P = A \rho^{\gamma}$ with $\gamma\ge1$. Our main result extends the one in [13] on the quantum Navier-Stokes equations to the CNSLLM system.

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CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES^*

Shanli YE, Zhihui ZHOU

数学物理学报(英文版). 2023 (1): 43-50. DOI: 10.1007/s10473-023-0103-x

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For any $\alpha\in\mathbb{R}$, the logarithmic Bloch space $\mathscr{B}_{L^{\alpha}}$ consists of those functions $f$ which are analytic in the unit disk $\mathbb{D}$ with $\sup_{z\in\mathbb{D}}(1-|z|^2)\left(\log\frac{\rm e}{1-|z|^2}\right)^{\alpha}|f'(z)|<\infty.$ In this paper, we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space $\mathscr{B}_{L^{\alpha}}$ for all $\alpha\in\mathbb{R}$.

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DE RHAM DECOMPOSITION FOR RIEMANNIAN MANIFOLDS WITH BOUNDARY^*

Chengjie YU

数学物理学报(英文版). 2023 (1): 51-62. DOI: 10.1007/s10473-023-0104-9

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In this paper, we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the development of curves.

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THE BOHR-TYPE INEQUALITIES FOR HOLOMORPHIC MAPPINGS WITH A LACUNARY SERIES IN SEVERAL COMPLEX VARIABLES^*

Rouyuan Lin, Mingsheng Liu, Saminathan Ponnusamy

数学物理学报(英文版). 2023 (1): 63-79. DOI: 10.1007/s10473-023-0105-8

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In this paper, we mainly use the Fréchet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space, namely, mappings from $U^n$ to $U$ (resp. $U^n$ to $U^n$). In addition, we discuss whether or not there is a constant term in $f$, and we obtain two redefined Bohr inequalities in $U^n$. Finally, we redefine the Bohr inequality of the odd and even terms of the analytic function $f$ so as to obtain conclusions for two different higher-dimensional alternating series.

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MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*

Yan Li, Ruoxia Yao, Yarong Xia

数学物理学报(英文版). 2023 (1): 80-96. DOI: 10.1007/s10473-023-0106-7

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Soliton molecules (SMs) of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation are found by utilizing a velocity resonance ansatz to $N$-soliton solutions, which can transform to asymmetric solitons upon assigning appropriate values to some parameters. Furthermore, a double-peaked lump solution can be constructed with breather degeneration approach. By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions, various kinds of interactional structures are constructed; There include the soliton molecule (SM), the breather molecule (BM) and the soliton-breather molecule (SBM). Graphical investigation and theoretical analysis show that the interactions composed of SM, BM and SBM are inelastic.

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THE OPTIMAL REINSURANCE-INVESTMENT PROBLEM CONSIDERING THE JOINT INTERESTS OF AN INSURER AND A REINSURER UNDER HARA UTILITY^*

Yan Zhang, Peibiao Zhao, Huaren Zhou

数学物理学报(英文版). 2023 (1): 97-124. DOI: 10.1007/s10473-023-0107-6

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This paper focuses on an optimal reinsurance and investment problem for an insurance corporation which holds the shares of an insurer and a reinsurer. Assume that the insurer can purchase reinsurance from the reinsurer, and that both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset which are governed by the Heston model and are distinct from one another. We aim to find the optimal reinsurance-investment strategy by maximizing the expected Hyperbolic Absolute Risk Aversion (HARA) utility of the insurance corporation's terminal wealth, which is the weighted sum of the insurer's and the reinsurer's terminal wealth. The Hamilton-Jacobi-Bellman (HJB) equation is first established. However, this equation is non-linear and is difficult to solve directly by any ordinary method found in the existing literature, because the structure of this HJB equation is more complex under HARA utility. In the present paper, the Legendre transform is applied to change this HJB equation into a linear dual one such that the explicit expressions of optimal investment-reinsurance strategies for $-1\le \rho_i \le 1$ are obtained. We also discuss some special cases in a little bit more detail. Finally, numerical analyses are provided.

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OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES^*

Guiqiao XU, Yongping Liu, Dandan GUO

数学物理学报(英文版). 2023 (1): 125-142. DOI: 10.1007/s10473-023-0108-5

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This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space $L_\infty[-1,1]$ and weighted spaces $L_{p,\omega}[-1,1], \ 1\le p< \infty$, with $\omega$ being a continuous integrable weight function in $(-1,1)$. We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal. We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

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A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS^*

Yezhou Li, Heqing Sun

数学物理学报(英文版). 2023 (1): 143-155. DOI: 10.1007/s10473-023-0109-4

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Let $f$ be an entire solution of the Tumura-Clunie type non-linear delay differential equation. We mainly investigate the dynamical properties of Julia sets of $f$, and the lower bound estimates of the measure of related limiting directions is verified.

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BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS^*

Haiyang Jin, Kaiying Xu

数学物理学报(英文版). 2023 (1): 156-168. DOI: 10.1007/s10473-023-0110-y

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This paper is concerned with the parabolic-parabolic-elliptic system $\begin{equation*} \begin{cases} u_t=\Delta u-\chi \nabla \cdot \left(u\nabla v\right) +\xi_1\nabla \cdot \left(u^m\nabla w\right), &x\in \Omega,t>0,\\ v_t=\Delta v+\xi_2 \nabla \cdot \left(v\nabla w\right)+u-v,&x\in \Omega,t>0,\\[2mm] 0=\Delta w+u-\frac{1}{|\Omega|}\int_\Omega u, \int_\Omega w=0,&x\in \Omega,t>0,\\[3mm] \frac{\partial u}{\partial\nu}=\frac{\partial v}{\partial\nu}=\frac{\partial w}{\partial\nu}=0, &x\in\partial\Omega, t>0,\\[2mm] u(x,0)=u_0(x),v(x,0)=v_0(x), &x\in \Omega \end{cases} \end{equation*}$ in a bounded domain $\Omega \subset \mathbb{R}^{n}$ with a smooth boundary, where the parameters $\chi,\xi_1,\xi_2 $ are positive constants and $m\geq 1$. Based on the coupled energy estimates, the boundedness of the global classical solution is established in any dimensions ($n\geq 1$) provided that $m>1$.

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GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE^*

Pengfei Pan, Hongwei Xu, Entao Zhao

数学物理学报(英文版). 2023 (1): 169-183. DOI: 10.1007/s10473-023-0111-x

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In this paper, we mainly study the global rigidity theorem of Riemannian submanifolds in space forms. Let $M^n(n \geq 3)$ be a complete minimal submanifold in the unit sphere $ S^{n+p}(1) $. For $\lambda \in [0,\frac{n}{2-1/p})$, there is an explicit positive constant $C(n, p, \lambda )$, depending only on $n,p,\lambda $, such that, if $ \int_{M} S^{n/2} {\rm d}M < \infty, \int_{M}(S-\lambda )_{+}^{n/2}{\rm d}M<C(n, p, \lambda), $ then $M^n$ is a totally geodetic sphere, where $S$ denotes the square of the second fundamental form of the submanifold and $f_+=\max\{0,f\}$. Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space $ R^{n+p}$.

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A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES^*

Duong Viet Thong, Vu Tien Dung

数学物理学报(英文版). 2023 (1): 184-204. DOI: 10.1007/s10473-023-0112-9

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In this paper, we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method. Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in [0; 1]. The purpose of this work is to continue working in this direction, we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be $1$. Under suitable mild conditions, we establish the weak convergence of the proposed algorithm. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Finally, some numerical illustrations are given to confirm the theoretical analysis.

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GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

Mingying zhong

数学物理学报(英文版). 2023 (1): 205-236. DOI: 10.1007/s10473-023-0113-8

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The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three dimensional space are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.

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THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE NON-ISENTROPIC IMPROVED AW-RASCLE-ZHANG MODEL^*

Weifeng Jiang, Tingting Chen, Tong Li, Zhen Wang

数学物理学报(英文版). 2023 (1): 237-258. DOI: 10.1007/s10473-023-0114-7

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In this paper, we study the Radon measure initial value problem for the non-isentropic improved Aw-Rascle-Zhang model. For arbitrary convex $F(u)$ in this model we construct the Riemann solutions by elementary waves and $\delta$-shock waves using the method of generalized characteristic analysis. We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piecewise constants. Moreover, we analyze different kinds of wave interactions, including the interactions of the $\delta$-shock waves with elementary waves.

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A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*

Bo Han, Manseob Lee

数学物理学报(英文版). 2023 (1): 259-288. DOI: 10.1007/s10473-023-0115-6

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In this paper, we define a generalized Lipschitz shadowing property for flows and prove that a flow $\phi$ generated by a $C^1$ vector field $X$ on a closed Riemannian manifold $M$ has this generalized Lipschitz shadowing property if and only if it is structurally stable.

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QUATERNIONIC SLICE REGULAR FUNCTIONS AND QUATERNIONIC LAPLACE TRANSFORMS^*

Gang HAN

数学物理学报(英文版). 2023 (1): 289-302. DOI: 10.1007/s10473-023-0116-5

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The functions studied in the paper are the quaternion-valued functions of a quaternionic variable. It is shown that the left slice regular functions and right slice regular functions are related by a particular involution, and that the intrinsic slice regular functions play a central role in the theory of slice regular functions. The relation between left slice regular functions, right slice regular functions and intrinsic slice regular functions is revealed. As an application, the classical Laplace transform is generalized naturally to quaternions in two different ways, which transform a quaternion-valued function of a real variable to a left or right slice regular function. The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.

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EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS^*

Yuanyuan Luo, Dongmei Gao, Jun Wang

数学物理学报(英文版). 2023 (1): 303-323. DOI: 10.1007/s10473-023-0117-4

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We study the Choquard equation $\begin{equation*}\label{a-1} -\Delta u+V(x)u=b(x)\int_{{\mathbb{R}^{3}}}{\frac{{{\left| u(y) \right|}^{2}}}{{{\left| x-y \right|}}}{\rm d}y}{u},\ x\in\mathbb{R}^{3}, \end{equation*}$ where $ V(x)=V_1(x)$, $ b(x)=b_1(x) $ for $ x_1>0 $ and $ V(x)=V_2(x), b(x)=b_2(x) $ for $ x_1<0 $, and $ V_1 $, $ V_2 $, $ b_1 $ and $ b_2 $ are periodic in each coordinate direction. Under some suitable assumptions, we prove the existence of a ground state solution of the equation. Additionally, we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

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THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE*

Huafei DI, Weijie Rong

数学物理学报(英文版). 2023 (1): 324-348. DOI: 10.1007/s10473-023-0118-3

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This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation $u_{t}+(-\Delta)^{s_{1}} u_{t}+\beta(-\Delta)^{s_{2}}u=F(u,x,t)$ subject to random Gaussian white noise for initial and final data. Under the suitable assumptions $s_{1}$, $s_{2}$ and $\beta$, we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard, which are mainly driven by random noise. Moreover, we propose the Fourier truncation method for stabilizing the above ill-posed problems. We derive an error estimate between the exact solution and its regularized solution in an $\mathbb{E}\parallel\cdot\parallel^{2}_{H^{s_{2}}}$ norm, and give some numerical examples illustrating the effect of above method.

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AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*

Xiuwei YIN

数学物理学报(英文版). 2023 (1): 349-362. DOI: 10.1007/s10473-023-0119-2

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In this paper, we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling. As an application, we also obtain the shift Harnack inequalities.

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MAXWELL-EINSTEIN METRICS ON COMPLETIONS OF CERTAIN ${\bf C}^*$ BUNDLES^*

Zhuangdan Guan

数学物理学报(英文版). 2023 (1): 363-372. DOI: 10.1007/s10473-023-0120-9

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In this paper, we prove that for some completions of certain fiber bundles there is a Maxwell-Einstein metric conformally related to any given K\"ahler class.

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IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*

Zhuang Wang, Haiqing Xu

数学物理学报(英文版). 2023 (1): 373-386. DOI: 10.1007/s10473-023-0121-8

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Let $\mathbb{X}$ be a Jordan domain satisfying certain hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ in [A. Koski, J. Onninen, Sobolev homeomorphic extensions, J. Eur. Math. Soc. 23 (2021) 4065-4089, Theorem 3.1].

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BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*

Shengkun Wu, Dechao Zhen

数学物理学报(英文版). 2023 (1): 387-408. DOI: 10.1007/s10473-023-0122-7

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In this paper, we study band-dominated operators on Bergman-type spaces and prove that the $C^*$-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions. On the Bergman space and the Fock space, we show that the $C^*$-algebra of band-dominated operators equals the Toeplitz algebra.

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LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS^*

Yuzhen kong, Zhiyuan cui, Dun zhao

数学物理学报(英文版). 2023 (1): 409-438. DOI: 10.1007/s10473-023-0123-6

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We study the ground states of attractive binary Bose-Einstein condensates with $N$ particles, which are trapped in the steep potential wells $\lambda V(x)$ in $\mathbb{R}^2$. We show that there exists a positive number $N_{*}$ such that if $N>N_{*}$, the system admits no ground state for any $\lambda>0$. Moreover, there exist two positive numbers, $M_{*}$ and $\lambda^*(N)$, such that if $N<M_{*}$, then for any $\lambda>\lambda^*(N)$, the system admits at least one ground state. As $\lambda\rightarrow\infty$, for any fixed $N<M_{*}$, we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

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THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS^*

Zhibo Huang, Minwei Luo, Zongxuan Chen

数学物理学报(英文版). 2023 (1): 439-449. DOI: 10.1007/s10473-023-0124-5

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By looking at the situation when the coefficients $P_{j}(z)$ $(j=1,2,\cdots,n-1)$ (or most of them) are exponential polynomials, we investigate the fact that all nontrivial solutions to higher order differential equations $f^{(n)}+P_{n-1}(z)f^{(n-1)}+\cdots+P_{0}(z)f=0$ are of infinite order. An exponential polynomial coefficient plays a key role in these results.

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UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*

Jianli XIANG, Guozheng YAN

数学物理学报(英文版). 2023 (1): 450-468. DOI: 10.1007/s10473-023-0125-4

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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. It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so it is impossible to reconstruct the location of the underlying scatterers. Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium, we consider different types of superpositions of incident waves to break the translation invariance property.

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