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The Steklov eigenproblem for a micropolar elastic solid 微极弹性固体的Steklov本征问题
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-02-26 DOI: 10.1016/j.jde.2026.114242
Bauyrzhan Derbissaly
{"title":"The Steklov eigenproblem for a micropolar elastic solid","authors":"Bauyrzhan Derbissaly","doi":"10.1016/j.jde.2026.114242","DOIUrl":"10.1016/j.jde.2026.114242","url":null,"abstract":"<div><div>We study the Steklov eigenvalue problem for a linear, isotropic micropolar (Cosserat) elastic solid, where the spectral parameter enters boundary conditions that link tangential tractions to tangential boundary fields. We formulate the problem in strong and weak forms, identify the Dirichlet-to-Neumann map on the boundary, and prove discreteness of the spectrum. Using a microlocal analysis of this map, we establish a Weyl law with an explicit coefficient expressed in terms of the Cosserat moduli. We also analyze spectral stability under high-frequency boundary perturbations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114242"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rotating waves for nonlinear wave equations with angular velocities on a positive-measure set 正测度集上角速度非线性波动方程的旋转波
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-01-26 DOI: 10.1016/j.jde.2026.114155
Yingdu Dong, Xiong Li
{"title":"Rotating waves for nonlinear wave equations with angular velocities on a positive-measure set","authors":"Yingdu Dong,&nbsp;Xiong Li","doi":"10.1016/j.jde.2026.114155","DOIUrl":"10.1016/j.jde.2026.114155","url":null,"abstract":"<div><div>In this paper, we focus on the existence of rotating wave solutions for a nonlinear wave equation on the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> with <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, which is a kind of traveling wave solutions on non-Euclidean spaces. The case when the angular velocity is larger than 1 is of particular focus, as it leads to an elliptic-hyperbolic mixed-type equation. Generally, the spectrum of a mixed-type linearized operator could behave badly, e.g., the spectrum is unbounded from below and above, and there may exist an accumulation at zero. The aim of this paper is to address the case with accumulation points in the spectrum, which leads to the ‘small divisor problem’. Owing to the geometric structure of the sphere and the good properties of the eigenvalues of the Laplacian on it, the accumulation can occur in a controlled manner if appropriate angular velocities are selected. Then we attack this issue through the Nash-Moser type iteration theorem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114155"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity 具有一般粘度和电阻率的二维MHD方程在Couette周围的稳定性阈值
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-02-04 DOI: 10.1016/j.jde.2026.114166
Fei Wang , Zeren Zhang
{"title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity","authors":"Fei Wang ,&nbsp;Zeren Zhang","doi":"10.1016/j.jde.2026.114166","DOIUrl":"10.1016/j.jde.2026.114166","url":null,"abstract":"<div><div>We address a threshold problem of the Couette flow <span><math><mo>(</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> in a uniform magnetic field <span><math><mo>(</mo><mi>β</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> for the 2D MHD equation on <span><math><mi>T</mi><mo>×</mo><mi>R</mi></math></span> with fluid viscosity <em>ν</em> and magnetic resistivity <em>μ</em>. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when <span><math><mn>0</mn><mo>&lt;</mo><mi>ν</mi><mo>≤</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>≤</mo><mn>1</mn></math></span>, we get a threshold <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></math></span> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>(</mo><mi>N</mi><mo>≥</mo><mn>4</mn><mo>)</mo></math></span>. When <span><math><mn>0</mn><mo>&lt;</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>≤</mo><mi>ν</mi><mo>≤</mo><mn>1</mn></math></span>, we obtain a threshold <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>,</mo><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>}</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>1</mn><mo>,</mo><msup><mrow><mi>ν</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>}</mo></math></span>, hence improving the results in <span><span>[19]</span></span>, <span><span>[14]</span></span>, <span><span>[22]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114166"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime 本征弱扩散区空间非均匀Vlasov-Nordström-Fokker-Planck体系
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-01-23 DOI: 10.1016/j.jde.2026.114137
Shengchuang Chang , Shuangqian Liu , Tong Yang
{"title":"The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime","authors":"Shengchuang Chang ,&nbsp;Shuangqian Liu ,&nbsp;Tong Yang","doi":"10.1016/j.jde.2026.114137","DOIUrl":"10.1016/j.jde.2026.114137","url":null,"abstract":"<div><div>The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of relativistic velocity, presents a significant challenge in analysis for the spatially inhomogeneous counterpart.</div><div>In this paper, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system, without friction, maintains dynamically stable relative to the corresponding spatially homogeneous system. Our results are twofold: (1) we establish the existence of a unique global classical solution and characterize the asymptotic behavior of the spatially inhomogeneous system using a refined weighted energy method; (2) we directly verify the dynamic stability of the spatially inhomogeneous system in the framework of rescaled solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114137"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions 双重非线性非标准增长的抛物De Giorgi类：精确可积假设下的局部有界性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-02-17 DOI: 10.1016/j.jde.2026.114235
Simone Ciani , Eurica Henriques , Mariia O. Savchenko , Igor I. Skrypnik
{"title":"Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions","authors":"Simone Ciani ,&nbsp;Eurica Henriques ,&nbsp;Mariia O. Savchenko ,&nbsp;Igor I. Skrypnik","doi":"10.1016/j.jde.2026.114235","DOIUrl":"10.1016/j.jde.2026.114235","url":null,"abstract":"<div><div>We define a suitable class <span><math><mi>PDG</mi></math></span> of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Then we prove that members of <span><math><mi>PDG</mi></math></span> are locally bounded, under critical, sub-critical and limit growth conditions typical of singular and degenerate parabolic operators, with quantitative point-wise estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Uraltseva <span><span>[31]</span></span>. These local bounds are new in the critical case and sub-critical cases, and have been obtained without any qualitative boundedness assumption. In particular, our proof of local boundedness in the critical case is valid disregarding of any additional integrability conditions and covers both the classical <em>p</em>-Laplacian and the porous medium equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114235"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global dynamics of nonlocal dispersal systems on time-varying domains 时变域上非局部扩散系统的全局动力学
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-05-05 Epub Date: 2026-01-28 DOI: 10.1016/j.jde.2026.114144
Xiandong Lin , Hailong Ye , Xiao-Qiang Zhao
{"title":"Global dynamics of nonlocal dispersal systems on time-varying domains","authors":"Xiandong Lin ,&nbsp;Hailong Ye ,&nbsp;Xiao-Qiang Zhao","doi":"10.1016/j.jde.2026.114144","DOIUrl":"10.1016/j.jde.2026.114144","url":null,"abstract":"<div><div>We propose a class of nonlocal dispersal systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. We first establish the comparison principle for generalized sub- and supersolutions of a class of nonautonomous nonlocal dispersal systems defined on the space of bounded measurable functions. Based on this, we develop a comprehensive framework to rigorously examine the threshold dynamics of the original system on asymptotically fixed and time-periodic domains. In the asymptotically unbounded case, we introduce a key auxiliary function to address the difficulties caused by the vanishing viscosity as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>, and the time-dependent coupling structure in the nonlocal kernels. This enables us to construct generalized subsolutions and derive the global threshold dynamics via the comparison principle. The findings may be of independent interest and the developed techniques are expected to find further applications in the related nonlocal dispersal problems. We also conduct numerical simulations for a practical model to illustrate our analytical results.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114144"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatiotemporal dynamics in a multi-strain epidemic model with fractional diffusion 具有分数扩散的多菌株流行病模型的时空动力学
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-04-25 Epub Date: 2026-01-09 DOI: 10.1016/j.jde.2026.114096
Peng Shi , Yan-Xia Feng , Wan-Tong Li , Fei-Ying Yang
{"title":"Spatiotemporal dynamics in a multi-strain epidemic model with fractional diffusion","authors":"Peng Shi ,&nbsp;Yan-Xia Feng ,&nbsp;Wan-Tong Li ,&nbsp;Fei-Ying Yang","doi":"10.1016/j.jde.2026.114096","DOIUrl":"10.1016/j.jde.2026.114096","url":null,"abstract":"<div><div>Recent studies indicate that in many epidemics, the strains (bacterial or viral) of disease-causing pathogens exhibit significant diversity, and human mobility patterns follow scale-free, nonlocal dynamics characterized by heavy-tailed distributions such as Lévy flights. To investigate the long-range geographical spread of multi-strain epidemics, this article proposes a multi-strain susceptible-infected-susceptible (SIS) model incorporating fractional diffusion. The central questions addressed in our study include the competitive exclusion and coexistence of multiple strains, as well as the influence of fractional powers and dispersal rates on the asymptotic behavior of equilibrium solutions. Our analysis demonstrates that: (i) the basic reproduction number acts as a threshold for disease extinction; (ii) the invasion number serves as a threshold for both the existence and stability of the coexistence equilibrium and the stability of single-strain endemic equilibria. Additionally, we examine the effect of home and hospital isolation measures on disease transmission.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114096"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Novel convergence of solutions to 1D compressible Euler equations with spatiotemporal damping in critical case 临界情况下具有时空阻尼的一维可压缩欧拉方程解的新颖收敛性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-04-25 Epub Date: 2026-01-13 DOI: 10.1016/j.jde.2026.114094
Yang Cai , Changchun Liu , Ming Mei , Zejia Wang
{"title":"Novel convergence of solutions to 1D compressible Euler equations with spatiotemporal damping in critical case","authors":"Yang Cai ,&nbsp;Changchun Liu ,&nbsp;Ming Mei ,&nbsp;Zejia Wang","doi":"10.1016/j.jde.2026.114094","DOIUrl":"10.1016/j.jde.2026.114094","url":null,"abstract":"<div><div>This paper is concerned with the Cauchy problem for 1D compressible Euler equations with spatiotemporal damping in the critical case. We prove the existence of the solutions and their new convergence to the special diffusion waves by the technical time-weighted energy method, where the convergence rates are dependent on the spatial state of the spatiotemporal damping as <span><math><mi>x</mi><mo>→</mo><mo>±</mo><mo>∞</mo></math></span>. These convergence results significantly improve and develop the previous studies of Geng et al. (2020) <span><span>[10]</span></span> and Matsumura and Nishihara (2024) <span><span>[24]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114094"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Increasing stability for inverse acoustic source problems in the time domain 提高时域反声源问题的稳定性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-04-25 Epub Date: 2026-01-16 DOI: 10.1016/j.jde.2026.114114
Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang
{"title":"Increasing stability for inverse acoustic source problems in the time domain","authors":"Chun Liu ,&nbsp;Suliang Si ,&nbsp;Guanghui Hu ,&nbsp;Bo Zhang","doi":"10.1016/j.jde.2026.114114","DOIUrl":"10.1016/j.jde.2026.114114","url":null,"abstract":"<div><div>This paper is concerned with the inverse source problems for the acoustic wave equation in the full space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114114"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary 具有navier -滑移边界的无穷长管道中Leray问题的一个改进唯一性结果
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2026-04-25 Epub Date: 2026-01-14 DOI: 10.1016/j.jde.2026.114108
Zijin Li , Ning Liu , Taoran Zhou
{"title":"A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary","authors":"Zijin Li ,&nbsp;Ning Liu ,&nbsp;Taoran Zhou","doi":"10.1016/j.jde.2026.114108","DOIUrl":"10.1016/j.jde.2026.114108","url":null,"abstract":"<div><div>We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe <span><math><mi>D</mi><mo>=</mo><mi>Σ</mi><mo>×</mo><mi>R</mi></math></span>. We show that if the flux Φ of the solution is no larger than a critical value that is <em>independent with the friction ratio</em> of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio <span><math><mi>α</mi><mo>∈</mo><mo>]</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, and it is surprising since the prescribed uniqueness breaks down immediately when <span><math><mi>α</mi><mo>=</mo><mn>0</mn></math></span>, even if <span><math><mi>Φ</mi><mo>=</mo><mn>0</mn></math></span>.</div><div>Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux <span><math><msub><mrow><mi>Φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>16</mn></mrow></mfrac></math></span> provided that Σ is a unit disk.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114108"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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