Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Homogenization in 3D thin domains with oscillating boundaries of different orders","authors":"José M. Arrieta ,&nbsp;Jean Carlos Nakasato ,&nbsp;Manuel Villanueva-Pesqueira","doi":"10.1016/j.na.2024.113667","DOIUrl":"10.1016/j.na.2024.113667","url":null,"abstract":"<div><div>This paper presents an extension of the unfolding operator technique, initially applied to two-dimensional domains, to the realm of three-dimensional thin domains. The advancement of this methodology is pivotal, as it enhances our understanding and analysis of three-dimensional geometries, which are crucial in various practical fields such as engineering and physics. Our work delves into the asymptotic behavior of solutions to a reaction–diffusion equation with Neumann boundary conditions set within such a oscillatory 3-dimensional thin domain. The method introduced enables the deduction of effective problems across all scenarios, tackling the intrinsic complexity of these domains. This complexity is especially pronounced due to the possibility of diverse types of oscillations occurring along their boundaries.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113667"},"PeriodicalIF":1.3,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425075","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}

{"title":"A Blaschke–Petkantschin formula for linear and affine subspaces with application to intersection probabilities","authors":"Emil Dare ,&nbsp;Markus Kiderlen ,&nbsp;Christoph Thäle","doi":"10.1016/j.na.2024.113672","DOIUrl":"10.1016/j.na.2024.113672","url":null,"abstract":"<div><div>Consider a uniformly distributed random linear subspace <span><math><mi>L</mi></math></span> and a stochastically independent random affine subspace <span><math><mi>E</mi></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, both of fixed dimension. For a natural class of distributions for <span><math><mi>E</mi></math></span> we show that the intersection <span><math><mrow><mi>L</mi><mo>∩</mo><mi>E</mi></mrow></math></span> admits a density with respect to the invariant measure. This density depends only on the distance <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>E</mi><mo>∩</mo><mi>L</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mrow><mi>L</mi><mo>∩</mo><mi>E</mi></mrow></math></span> to the origin and is derived explicitly. It can be written as the product of a power of <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>E</mi><mo>∩</mo><mi>L</mi><mo>)</mo></mrow></mrow></math></span> and a part involving an incomplete beta integral. Choosing <span><math><mi>E</mi></math></span> uniformly among all affine subspaces of fixed dimension hitting the unit ball, we derive an explicit density for the random variable <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>E</mi><mo>∩</mo><mi>L</mi><mo>)</mo></mrow></mrow></math></span> and study the behavior of the probability that <span><math><mrow><mi>E</mi><mo>∩</mo><mi>L</mi></mrow></math></span> hits the unit ball in high dimensions. Lastly, we show that our result can be extended to the setting where <span><math><mi>E</mi></math></span> is tangent to the unit sphere, in which case we again derive the density for <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>E</mi><mo>∩</mo><mi>L</mi><mo>)</mo></mrow></mrow></math></span>. Our probabilistic results are derived by means of a new integral–geometric transformation formula of Blaschke–Petkantschin type.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113672"},"PeriodicalIF":1.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global low regularity solutions to the Benjamin equation in weighted spaces","authors":"Sergey Shindin,&nbsp;Nabendra Parumasur","doi":"10.1016/j.na.2024.113674","DOIUrl":"10.1016/j.na.2024.113674","url":null,"abstract":"<div><div>We show that the Benjamin equation is globally well-posed for real-valued data in the weighted space <span><span><span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>∩</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>s</mi><mo>−</mo><mn>2</mn><mi>r</mi></mrow></msubsup><mo>≔</mo><mrow><mo>{</mo><mrow><mi>u</mi><mspace></mspace><mo>|</mo><mspace></mspace><msub><mrow><mo>‖</mo><mi>u</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></mrow></msub><mo>+</mo><msub><mrow><mo>‖</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>ξ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mrow><mo>|</mo><mi>ξ</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mrow><mo>(</mo><mi>s</mi><mo>−</mo><mn>2</mn><mi>r</mi><mo>)</mo></mrow></mrow></msup><mi>d</mi><mi>ξ</mi><mo>)</mo></mrow></mrow></msub><mo>&lt;</mo><mi>∞</mi></mrow><mo>}</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mn>0</mn><mo>≤</mo><mi>r</mi></mrow></math></span> and <span><math><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mi>r</mi><mo>&lt;</mo><mi>s</mi></mrow></math></span>. The proof is based on direct extensions of standard linear and bilinear estimates originated in Kenig et al. (1993), Kenig et al. (1996), Linares (1999), Kozono et al. (2001), Colliander et al. (2003), Li and Wu (2010) to the weighted settings.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113674"},"PeriodicalIF":1.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323507","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}

{"title":"Analytical solutions to the free boundary problem of a two-phase model with radial and cylindrical symmetry","authors":"Hongxia Xue,&nbsp;Jianwei Dong","doi":"10.1016/j.na.2024.113670","DOIUrl":"10.1016/j.na.2024.113670","url":null,"abstract":"<div><div>In this paper, we study the free boundary problem of an inviscid two-phase model, where we take the pressure function as <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>ρ</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>γ</mi></mrow></msup><mo>+</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>≥</mo><mn>1</mn></mrow></math></span>) with <span><math><mi>n</mi></math></span> and <span><math><mi>ρ</mi></math></span> being the densities of two phases. First, we construct some self-similar analytical solutions for the <span><math><mi>N</mi></math></span>-dimensional radially symmetric case by using some ansatzs, and investigate the spreading rate of the free boundary by using the method of averaged quantities. Second, we extend the results of the <span><math><mi>N</mi></math></span>-dimensional radially symmetric case to the three-dimensional cylindrically symmetric case. Third, we present some analytical solutions for the three-dimensional cylindrically symmetric model with a Coriolis force. From the analytical solutions constructed in this paper, we find that the Coriolis force can prevent the free boundary from spreading out infinitely.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113670"},"PeriodicalIF":1.3,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001895/pdfft?md5=f5c63e293b0091e1cef7e731ee5a5250&pid=1-s2.0-S0362546X24001895-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thin film equations with nonlinear deterministic and stochastic perturbations","authors":"Oleksiy Kapustyan ,&nbsp;Olha Martynyuk ,&nbsp;Oleksandr Misiats ,&nbsp;Oleksandr Stanzhytskyi","doi":"10.1016/j.na.2024.113646","DOIUrl":"10.1016/j.na.2024.113646","url":null,"abstract":"<div><p>In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovich noise, as well as nonlinear colored Wiener noise. By means of Trotter–Kato-type decomposition into deterministic and stochastic parts, we couple both of these dynamics via a discrete-in-time scheme, and establish its convergence to a non-negative weak martingale solution.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113646"},"PeriodicalIF":1.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001652/pdfft?md5=f3d21fbe23f0caa335b0a9f697a81c70&pid=1-s2.0-S0362546X24001652-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the boundary blow-up problem for real (n−1) Monge–Ampère equation","authors":"Jingwen Ji ,&nbsp;Haiyun Deng ,&nbsp;Feida Jiang","doi":"10.1016/j.na.2024.113669","DOIUrl":"10.1016/j.na.2024.113669","url":null,"abstract":"<div><p>In this paper, we establish a necessary and sufficient condition for the solvability of the real <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span> Monge–Ampère equation <span><math><mrow><mover><mrow><mo>det</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>n</mi></mrow></mover><mrow><mo>(</mo><mi>Δ</mi><mi>u</mi><mi>I</mi><mo>−</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> in bounded domains with infinite Dirichlet boundary condition. The <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span> Monge–Ampère operator is derived from geometry and has recently received much attention. Our result embraces the case <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> where <span><math><mrow><mi>h</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span> is positive and <span><math><mi>f</mi></math></span> satisfies the Keller–Osserman type condition. We describe the asymptotic behavior of the solution by constructing suitable sub-solutions and super-solutions, and obtain a uniqueness result in star-shaped domains by using a scaling technique.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113669"},"PeriodicalIF":1.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001883/pdfft?md5=dcb2b703c48c88a6c661fc63e5774351&pid=1-s2.0-S0362546X24001883-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ohta–Kawasaki energy for amphiphiles: Asymptotics and phase-field simulations","authors":"Qiang Du ,&nbsp;James M. Scott ,&nbsp;Zirui Xu","doi":"10.1016/j.na.2024.113665","DOIUrl":"10.1016/j.na.2024.113665","url":null,"abstract":"<div><p>We study the minimizers of a degenerate case of the Ohta–Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symmetric candidates which give us insights into the asymptotic behaviors of energy minimizers in the large mass limit. In order to numerically study the problems that are analytically challenging, we propose a phase-field reformulation which is shown to Gamma-converge to the original sharp interface model. Our phase-field simulations and asymptotic results suggest that the energy minimizers exhibit behaviors similar to the self-assembly of amphiphiles, including the formation of lipid bilayer membranes.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113665"},"PeriodicalIF":1.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001846/pdfft?md5=c1e8f89875e4f78c3319ad9c2f245a48&pid=1-s2.0-S0362546X24001846-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large global solutions to the three dimensional compressible flow of liquid crystals","authors":"Xiaoping Zhai","doi":"10.1016/j.na.2024.113657","DOIUrl":"10.1016/j.na.2024.113657","url":null,"abstract":"<div><p>The purpose of this paper is to provide a class of large initial data which generates global solutions of the compressible flow of liquid crystals in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. This class of data relax the smallness restriction imposed on the initial incompressible velocity. Moreover, the result improve considerably the work by Hu and Wu [SIAM J. Math. Anal., 45 (2013), 2678-2699].</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113657"},"PeriodicalIF":1.3,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001767/pdfft?md5=7de785471e6e5046dbf64fd8ee14f840&pid=1-s2.0-S0362546X24001767-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation","authors":"Yuusuke Sugiyama","doi":"10.1016/j.na.2024.113658","DOIUrl":"10.1016/j.na.2024.113658","url":null,"abstract":"<div><p>In this paper, we consider the 1D Euler equation with time and space dependent damping term <span><math><mrow><mo>−</mo><mi>a</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mi>v</mi></mrow></math></span>. It has long been known that when <span><math><mrow><mi>a</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is a positive constant or 0, the solution exists globally in time or blows up in finite time, respectively. In this paper, we prove that those results are invariant with respect to time and space dependent perturbations. We suppose that the coefficient <span><math><mi>a</mi></math></span> satisfies the following condition <span><span><span><math><mrow><mrow><mo>|</mo><mi>a</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>|</mo></mrow><mo>≤</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are integrable functions with <span><math><mi>t</mi></math></span> and <span><math><mi>x</mi></math></span>. Under this condition, we show the global existence and the blow-up with small initial data, when <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> respectively. The key of the proof is to divide space into time-dependent regions, using characteristic curves.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113658"},"PeriodicalIF":1.3,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001779/pdfft?md5=9f5946837a904defdc71f1e5354348c9&pid=1-s2.0-S0362546X24001779-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces","authors":"Germán Fonseca,&nbsp;Oscar Riaño,&nbsp;Guillermo Rodriguez-Blanco","doi":"10.1016/j.na.2024.113653","DOIUrl":"10.1016/j.na.2024.113653","url":null,"abstract":"<div><p>We consider the initial value problem associated to the low dispersion fractionary Benjamin–Bona–Mahony equation, fBBM. Our aim is to establish local persistence results in weighted Sobolev spaces and to obtain unique continuation results that imply that those results above are sharp. Hence, arbitrary polynomial type decay is not preserved by the fBBM flow.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113653"},"PeriodicalIF":1.3,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X2400172X/pdfft?md5=deedf93280597ef7b37c6bea9b954b83&pid=1-s2.0-S0362546X2400172X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}