Journal of Mathematical Analysis and Applications最新文献

{"title":"Asymptotic behavior of α-entropy solutions to the thin film equation on the sphere","authors":"Roman Taranets ,&nbsp;Marina Chugunova ,&nbsp;Hangjie Ji","doi":"10.1016/j.jmaa.2026.130491","DOIUrl":"10.1016/j.jmaa.2026.130491","url":null,"abstract":"<div><div>We investigate the existence and behavior of <em>α</em>-entropy solutions to the double-degenerate thin-film equation, which models viscous coating flows on spherical surfaces. Our results show that these solutions exhibit both finite-speed propagation and a waiting-time phenomenon. Furthermore, we derive an upper bound for the interface propagation rate and a lower bound for the waiting time. Numerical simulations are also presented to support the analytical results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130491"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameter estimation for a stochastic pseudo-parabolic partial differential equation","authors":"Yang Cao ,&nbsp;Yuxiu Liu ,&nbsp;Chengyuan Qu","doi":"10.1016/j.jmaa.2026.130490","DOIUrl":"10.1016/j.jmaa.2026.130490","url":null,"abstract":"<div><div>This paper focuses on the parameter estimation problems associated with stochastic pseudo-parabolic partial differential equations (SPPDEs) driven by additive time-space white noise. Our investigation encompasses both MLE-like estimators and trajectory fitting estimators (TFEs), particularly when measurements are conducted in the spectral domain. Through a rigorous asymptotic analysis of these estimators, we establish their strong consistency and asymptotic normality. The unique third-order term in the SPPDE introduces significant challenges and necessitates novel findings. Notably, our work diverges from existing literature in its examination of the asymptotic behavior of TFEs as both the number of Fourier modes and time approach infinity, highlighting a distinct asymptotic regime.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130490"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A lower index bilinear estimate for the quadratic Schrödinger equation and application for its half line problem","authors":"Shenghao Li ,&nbsp;Xin Yang","doi":"10.1016/j.jmaa.2026.130486","DOIUrl":"10.1016/j.jmaa.2026.130486","url":null,"abstract":"<div><div>We prove the local well-posedness of the initial boundary value problem for the nonlinear quadratic Schrödinger equation under low initial-boundary regularity assumptions via the boundary integral operator method introduced by Bona-Sun-Zhang <span><span>[4]</span></span>. The key ingredient in our study is to generalize a special extension for the boundary integral operator which can fit lower regularity assumptions in <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>b</mi></mrow></msup></math></span> spaces comparing to the “zero” extension approach introduced in <span><span>[13]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130486"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium","authors":"Maarten V. de Hoop ,&nbsp;Kundan Kumar","doi":"10.1016/j.jmaa.2026.130416","DOIUrl":"10.1016/j.jmaa.2026.130416","url":null,"abstract":"<div><div>We present a mixed dimensional model for a fractured poro-elastic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a Darcy type model that follows the cubic law for permeability. The bulk poro-elasticity is governed by fully dynamic Biot equations. The resulting model is a mixed dimensional type where the fracture flow on a surface is coupled to a bulk flow and geomechanics model. The particularity of the work here is in considering fully dynamic Biot equation, that is, including an inertia term, and the contact mechanics including friction for the fracture surface. We prove the well-posedness of the continuous model.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130416"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ground state solutions and asymptotic behavior for a nonlocal Kirchhoff–Choquard equation with variable potential in R3","authors":"Mohammad Saeid Abolhassanifar ,&nbsp;Reza Saadati ,&nbsp;Mohammad Bagher Ghaemi ,&nbsp;Donal O'Regan","doi":"10.1016/j.jmaa.2026.130445","DOIUrl":"10.1016/j.jmaa.2026.130445","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We investigate a class of nonlinear nonlocal problems that integrate two complex mechanisms: Kirchhoff-type nonlocal diffusion and Choquard-type critical convolution nonlinearity involving the Hardy–Littlewood–Sobolev (HLS) critical exponent. Specifically, we consider the following equation in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; is the Riesz potential, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a positive, asymptotically constant potential. This formulation simultaneously captures &lt;em&gt;Kirchhoff-type nonlocality&lt;/em&gt; through the energy-dependent coefficient of the Laplacian, and &lt;em&gt;Choquard criticality&lt;/em&gt; via a convolution nonlinearity with critical exponent &lt;span&gt;&lt;math&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;By combining variational methods, Pohožaev-type identities, and global compactness techniques adapted to this doubly nonlocal setting, we prove the existence of positive ground state solutions in both subcritical and critical cases. Moreover, we analyze the asymptotic behavior as the nonlocal parameters approach their critical limits, &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130445"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and convergence analysis of reduced-order finite difference schemes for a class of nonlinear time-fractional partial differential equations","authors":"Huanrong Li,&nbsp;Wei Zhao,&nbsp;Xiaohua Zhang","doi":"10.1016/j.jmaa.2026.130465","DOIUrl":"10.1016/j.jmaa.2026.130465","url":null,"abstract":"<div><div>This paper is dedicated to developing reduced-order finite difference (ROFD) schemes for solving a class of nonlinear partial differential equations with Caputo-type time-fractional order <em>α</em> (<span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></math></span>) in both one-dimensional and two-dimensional spaces. The Caputo-type time derivative is approximated using the L1 scheme, while spatial derivatives are discretized via the central finite difference (FD) approach, establishing the classical FD schemes. By employing the proper orthogonal decomposition technique, the ROFD schemes are designed to systematically reduce computational complexity. Through rigorous theoretical analysis of the stability and convergence properties of both the FD and ROFD schemes, combined with an extensive series of numerical experiments, we demonstrate that the proposed ROFD schemes significantly decrease computational costs while preserving optimal accuracy, which establishes them as highly efficient tools for solving time-fractional partial differential equations (FPDEs). In particular, the numerical results are in excellent agreement with the theoretical predictions, thereby further substantiating the effectiveness and reliability of the proposed ROFD methods. This work not only enriches the numerical approaches for solving time-FPDEs but also establishes a robust foundation for extending the application of ROFD techniques to address more intricate fractional-order models across diverse scientific and engineering fields.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130465"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rearrangement-invariant norms commuting with dilations","authors":"Santiago Boza ,&nbsp;Martin Křepela ,&nbsp;Javier Soria","doi":"10.1016/j.jmaa.2026.130469","DOIUrl":"10.1016/j.jmaa.2026.130469","url":null,"abstract":"<div><div>We study rearrangement-invariant spaces <em>X</em> over <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> for which there exists a function <span><math><mi>h</mi><mo>:</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>→</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> such that<span><span><span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msub><mi>f</mi><mo>‖</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>=</mo><mi>h</mi><mo>(</mo><mi>r</mi><mo>)</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>X</mi></mrow></msub></math></span></span></span> for all <span><math><mi>f</mi><mo>∈</mo><mi>X</mi></math></span> and all <span><math><mi>r</mi><mo>&gt;</mo><mn>0</mn></math></span>, where <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> is the dilation operator. It is shown that this may hold only if <span><math><mi>h</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>r</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup></math></span> for all <span><math><mi>r</mi><mo>&gt;</mo><mn>0</mn></math></span>, in which case the norm <span><math><msub><mrow><mo>‖</mo><mo>⋅</mo><mo>‖</mo></mrow><mrow><mi>X</mi></mrow></msub></math></span> is called <em>p</em>-homogeneous. We investigate which types of r.i. spaces satisfy this condition and show some important embedding properties.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130469"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A bifurcation phenomenon for the critical Laplace and p-Laplace equation in the ball","authors":"Francesca Dalbono ,&nbsp;Matteo Franca ,&nbsp;Andrea Sfecci","doi":"10.1016/j.jmaa.2026.130482","DOIUrl":"10.1016/j.jmaa.2026.130482","url":null,"abstract":"<div><div>We consider radial positive solutions for a class of quasilinear differential equations ruled by the <em>p</em>-Laplace differential operator with a critical weighted nonlinearity. We show that the problem undergoes a bifurcation phenomenon. We provide a new multiplicity result, even in the classical Laplace case. The proofs use the Fowler transformation and dynamical systems tools.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130482"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Free dilations of families of C0-semigroups and applications to evolution families","authors":"Raj Dahya","doi":"10.1016/j.jmaa.2026.130460","DOIUrl":"10.1016/j.jmaa.2026.130460","url":null,"abstract":"<div><div>Commuting families of contractions or contractive <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroups on Hilbert spaces often fail to admit power dilations resp. simultaneous unitary dilations which are themselves commutative (see <span><span>[44]</span></span>, <span><span>[14]</span></span>). In the <em>non-commutative</em> setting, Sz.-Nagy <span><span>[59]</span></span> and Bożejko <span><span>[5]</span></span> provided means to dilate arbitrary families of contractions. The present work extends these discrete-time results to families <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>i</mi><mo>∈</mo><mi>I</mi></mrow></msub></math></span> of contractive <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroups. We refer to these dilations as continuous-time <em>free unitary dilations</em> and present three distinct approaches to obtain them: 1) An explicit derivation applicable to semigroups that arise as interpolations; 2) A full proof with an explicit construction, via the theory of co-generators à la Słociński <span><span>[53]</span></span>, <span><span>[54]</span></span>; and 3) A second full proof based on the abstract structure of semigroups, which admits a natural reformulation to semigroups defined over topological free products of <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>⩾</mo><mn>0</mn></mrow></msub></math></span> and leads to various residuality results. In 2) a II^nd free dilation theorem for topologised index sets is developed via a reformulation of the Trotter–Kato theorem for co-generators. As an application of this we demonstrate how evolution families can be reduced to continuously monitored processes subject to temporal change, à la the quantum Zeno effect <span><span>[21]</span></span>, <span><span>[22]</span></span>, <span><span>[23]</span></span>, <span><span>[29]</span></span>, <span><span>[36]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130460"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy estimates and velocity convergence of the Cucker-Smale model with infinite particles","authors":"Kunning Zhang","doi":"10.1016/j.jmaa.2026.130463","DOIUrl":"10.1016/j.jmaa.2026.130463","url":null,"abstract":"<div><div>We study the quantitative estimate of the infinite-particle Cucker-Smale (IPCS) model and the kinetic CS model in a short-range communication kernel. First, we use the structure of the IPCS model to establish the quantitative estimate of energy. Second, the velocity convergence of each particle is obtained using energy estimation. Third, we use an approximate method to establish the existence and uniqueness of the solution to the IPCS model under unbounded initial data. Finally, we use the infinite-particle mean-field limit to derive the quantitative estimate of the kinetic CS model through the particle-in-cell method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130463"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}