Nonlinear Analysis-Theory Methods & Applications最新文献

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A Blaschke–Petkantschin formula for linear and affine subspaces with application to intersection probabilities 线性和仿射子空间的布拉什克-佩特康钦公式及其在交集概率中的应用
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-26 DOI: 10.1016/j.na.2024.113672
Emil Dare , Markus Kiderlen , Christoph Thäle
{"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}
引用次数: 0
Global low regularity solutions to the Benjamin equation in weighted spaces 加权空间中本杰明方程的全局低正则解
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-26 DOI: 10.1016/j.na.2024.113674
Sergey Shindin, Nabendra Parumasur
{"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}
引用次数: 0
Analytical solutions to the free boundary problem of a two-phase model with radial and cylindrical symmetry 具有径向和圆柱对称性的两相模型自由边界问题的解析解
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-23 DOI: 10.1016/j.na.2024.113670
Hongxia Xue, Jianwei Dong
{"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}
引用次数: 0
Thin film equations with nonlinear deterministic and stochastic perturbations 具有非线性确定性和随机扰动的薄膜方程
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-16 DOI: 10.1016/j.na.2024.113646
Oleksiy Kapustyan , Olha Martynyuk , Oleksandr Misiats , Oleksandr Stanzhytskyi
{"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}
引用次数: 0
On the boundary blow-up problem for real (n−1) Monge–Ampère equation 关于实(n-1)蒙盖-安培方程的边界膨胀问题
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-16 DOI: 10.1016/j.na.2024.113669
Jingwen Ji , Haiyun Deng , Feida Jiang
{"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}
引用次数: 0
Ohta–Kawasaki energy for amphiphiles: Asymptotics and phase-field simulations 双亲化合物的 Ohta-Kawasaki 能量:渐近和相场模拟
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-13 DOI: 10.1016/j.na.2024.113665
Qiang Du , James M. Scott , Zirui Xu
{"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}
引用次数: 0
Large global solutions to the three dimensional compressible flow of liquid crystals 液晶三维可压缩流动的大全局解决方案
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-12 DOI: 10.1016/j.na.2024.113657
Xiaoping Zhai
{"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}
引用次数: 0
Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation 具有时间和空间相关扰动的一维阻尼可压缩欧拉方程的全局存在性和炸毁问题
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-12 DOI: 10.1016/j.na.2024.113658
Yuusuke Sugiyama
{"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}
引用次数: 0
On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces 论加权索波列夫空间中具有低分散性的分式 BBM 方程的持续特性
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-09-04 DOI: 10.1016/j.na.2024.113653
Germán Fonseca, Oscar Riaño, Guillermo Rodriguez-Blanco
{"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}
引用次数: 0
Stability of the logarithmic Sobolev inequality and uncertainty principle for the Tsallis entropy 对数索波列夫不等式的稳定性和查里斯熵的不确定性原理
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-08-31 DOI: 10.1016/j.na.2024.113644
Takeshi Suguro
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