数学最新文献

{"title":"Q-learning promotes the evolution of fairness and generosity in the ultimatum game","authors":"Binjie Wu ,&nbsp;Shaofei Shen ,&nbsp;Jiafeng Wang ,&nbsp;Haibin Wan","doi":"10.1016/j.chaos.2025.116984","DOIUrl":"10.1016/j.chaos.2025.116984","url":null,"abstract":"<div><div>The traditional Q-learning algorithm has been widely applied to the study of cooperation in social dilemmas, however, few studies have utilized it in the context of the Ultimatum Game. To address this gap, this paper investigates the evolutionary Ultimatum Game by proposing a strategy-adjustment-based Q-learning algorithm. Through Monte Carlo simulations, we quantitatively confirm the significant influence of sensitivity factors (denoted as <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>) on fairness and generosity. Notably, compared to the conventional situation, the introduction of sensitivity factors, especially when <span><math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>≫</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>q</mi></mrow></msub></mrow></math></span>, leads to a marked increase in levels of fairness and generosity. Additionally, when <span><math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>≪</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>q</mi></mrow></msub></mrow></math></span>, the population gravitates toward empathy-driven strategies, further enhancing fairness. Conversely, we find that when <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> are approximately equal, fairness is undermined. These evolutionary dynamics provide deeper insights into the mechanisms underlying fairness and generosity in human behavior.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 116984"},"PeriodicalIF":5.6,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-driven system identification for piecewise dynamical systems via Sparse Identification Neural Ordinary Differential Equations","authors":"Zhang Chen ,&nbsp;Wei Zhu ,&nbsp;Hanlin Bian ,&nbsp;Guang Yang","doi":"10.1016/j.chaos.2025.117028","DOIUrl":"10.1016/j.chaos.2025.117028","url":null,"abstract":"<div><div>Traditional approaches to data-driven system identification typically focus on global information while neglecting the influence of local information. This oversight poses challenges to the model identification for piecewise dynamical systems. This paper introduces Sparse Identification Neural Ordinary Differential Equations (SI-NODEs), a novel framework for data-driven identification for piecewise dynamical systems. Neural Ordinary Differential Equations (NODEs) are initially employed to extract localized information. Utilizing reverse thinking, implicit NODEs are applied to identify points of imperfect fit which correspond to the piecewise points. Subsequently, the sparse identification or explicit NODEs are used to identify the differential equations for each data segment, thereby obtaining global information. This framework synergizes the fitting capabilities of implicit NODEs with the sparse regression or the flexible neural modeling of explicit NODEs. The uniqueness and convergence are rigorously proved about piecewise point identification. Compared to classical approaches such as Sparse Identification of Nonlinear Dynamics (SINDy) and Neural Ordinary Differential Equations (NODEs), the effectiveness and superiority of the proposed SI-NODEs framework are demonstrated by piecewise linear system, piecewise Lorenz system, and piecewise nonlinear system contains two-stroke and four-stroke oscillators, respectively. Robustness under noisy conditions is also verified using data with different noise levels.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117028"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Threshold dynamics of a stochastic single species model with two component Allee effects","authors":"Guijie Lan","doi":"10.1016/j.chaos.2025.116952","DOIUrl":"10.1016/j.chaos.2025.116952","url":null,"abstract":"<div><div>This paper establishes a stochastic population model incorporating two component Allee effects. For the deterministic model, we rigorously prove the existence and stability of equilibria. For the stochastic model, we derive the stochastic net reproductive rate <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup></math></span>, serving as a sharp threshold, that is, if <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the population is extinct almost surely, while <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>&gt;</mo><mn>1</mn></mrow></math></span> results in the population being strongly stochastically permanent.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 116952"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Joule heating effect on radiative heat oscillations over inlet-cone for cooling and thermal load of high-speed turbojet aircraft: Darcy Casson turbulence control model","authors":"Mhamed Benaissa ,&nbsp;Zia Ullah ,&nbsp;Md. Mahbub Alam ,&nbsp;Hanaa Abu-Zinadah ,&nbsp;Muhammad Ashraf ,&nbsp;Noureddine Elboughdiri ,&nbsp;Djamel Ghernaout ,&nbsp;Alsamani A.M. Salih ,&nbsp;Nidhal Ben Khedher","doi":"10.1016/j.chaos.2025.117019","DOIUrl":"10.1016/j.chaos.2025.117019","url":null,"abstract":"<div><div>Ohmic heating, heat dissipation and Darcy Forchheimer porous medium effects on turbulence of oscillatory heat and mass transfer along inlet heated cone in aircraft turbine and jet engines are investigated current problem. Darcy Forchheimer porous medium is applied to control turbulence of fluid flow, heat transfer and mass rate along inlet cone in aircraft engines. The transient Casson nanofluid model is used to enhance the heat transfer and flow control over inlet cone in turbo-jet aircraft engine. The flow controlling parameters are generated for physical behavior of thermal and flow boundary layers. The oscillatory motion of nanofluid and oscillatory heat transfer, oscillatory mass distribution, steady heat-mass transportation over inlet cone are calculated using Stokes transformation, complex variables and primitive formulation. The numerical and graphical results are deduced using significant parametric values of controlling factors. Lorentz force, Forchheimer porosity factor, Eckert number, Ohmic heating, solar radiation, thermophoresis, and Casson material parameter are utilized for oscillatory and turbulence flow of heat and mass transfer. The 2D behavior of streamlines and isothermal lines over inlet cone is examined. The following parametric range of <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>M</mi><mi>f</mi></msub><mo>≤</mo><mn>4.0</mn></math></span>, <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>F</mi><mi>r</mi></msub><mo>≤</mo><mn>1.2</mn></math></span>, <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>J</mi><mi>h</mi></msub><mo>≤</mo><mn>3.0</mn></math></span>, <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>E</mi><mi>c</mi></msub><mo>≤</mo><mn>6.0</mn></math></span>, <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>N</mi><mi>T</mi></msub><mo>≤</mo><mn>8.0</mn></math></span>, and <span><math><mn>0.0</mn><mo>≤</mo><msub><mi>R</mi><mi>d</mi></msub><mo>≤</mo><mn>20.0</mn></math></span> is applied to control turbulent heat and mass oscillations. The high flow of isotherms contour and streamlines is found for minor Lorentz, Forchheimer factor and large ohmic heating factor. Larger oscillating amplitude in fluid velocity and temperature-concentration variation is observed for each Forchheimer factor. Remarkable distribution in non-fluctuating heating magnitude and nanoparticle movement is observed for each solar radiating parameter. Prominent oscillating amplitude and turbulent fluctuation in heat and mass distribution is depicted for each Eckert, thermophoresis and Forchheimer parameters. The high rate of steady heat and mass transport is increased as radiating energy increases.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117019"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Arbitrary-order sensitivity analysis of frequency response functions using hypercomplex automatic differentiation and spectral finite elements","authors":"Juan David Navarro ,&nbsp;Juan C. Velasquez-Gonzalez ,&nbsp;Mauricio Aristizabal ,&nbsp;Arturo Montoya ,&nbsp;Harry R. Millwater ,&nbsp;David Restrepo","doi":"10.1016/j.amc.2025.129677","DOIUrl":"10.1016/j.amc.2025.129677","url":null,"abstract":"<div><div>Accurately computing sensitivities of Frequency Response Functions (FRFs) is crucial for analyzing the dynamic behavior of structures by enabling quantifying the impact that variations in geometry, material properties, and boundary conditions have on their dynamic response. However, one of the primary challenges in calculating accurate sensitivities lies in the numerical differentiation required to estimate the sensitivities of the FRFs. This paper presents a new method called the Hypercomplex Spectral Finite Elements Method (HYPAD-SFEM). HYPAD-SFEM combines the HYPercomplex Automatic Differentiation method (HYPAD) with the Spectral Finite Elements Method (SFEM) to compute highly accurate arbitrary-order sensitivities of the FRFs. To demonstrate and verify the method's performance and accuracy, we analyzed a truss structure under a harmonic axial load and compared the results with analytical equations, Finite Differences (FD), and traditional Automatic Differentiation (AD). Excellent agreement was observed between the computed displacements and their sensitivities, considering material properties, geometry, and boundary conditions. The application of HYPAD-SFEM was then extended to a more complex problem by performing shape sensitivity analysis of the dynamic behavior of a phononic lattice. Again, excellent agreement was found between HYPAD, FD and AD. In general, the proposed HYPAD-SFEM ensures high accuracy independent of the perturbation step selection, alleviating FD’s fundamental issues. Moreover, HYPAD-SFEM delivers superior computational performance when compared with traditional AD. Hence, HYPAD-SFEM provides an effective approach for FRF sensitivity analysis, facilitating design optimization, parameter tuning, robustness analysis, and model updating and validation in structural dynamics.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129677"},"PeriodicalIF":3.4,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144853010","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":"Turbulent and steady boundary layers and radiative heat transfer over magnetic coated elastic-polymer surface in drug-eluting polymeric stents: Powell-Eyring turbulence model","authors":"Zia Ullah ,&nbsp;Md. Mahbub Alam ,&nbsp;Essam.R. El-Zahar ,&nbsp;Sana Shahab ,&nbsp;Hanaa Abu-Zinadah ,&nbsp;Y.M. Mahrous ,&nbsp;Laila F. Seddek ,&nbsp;Abdullah A. Faqihi","doi":"10.1016/j.chaos.2025.117054","DOIUrl":"10.1016/j.chaos.2025.117054","url":null,"abstract":"<div><div>The stretching, magnetic coating and thermal radiating heat impact on conducting elastic-polymer surface has noticeable applications in drug-eluting polymer stents, biodegradable stents, tracheal stents, absorbable stents, vascular stents, coronary stents, and fabrication process of stents for enhanced heat and mass transport. Utilizing Powell-Eyring nanofluid, the amplitude, oscillation and phase change behavior in heating distribution and mass characteristics over elastic-polymer surface are deduced numerically. The polymer surface model is solved using dimensionless units, primitive-formulation, oscillatory stokes transformation, Gaussian-elimination technique and implicit finite difference method. The computational and tabular outcomes are deduced by using FORTAN tool and data is presented through Tecplot-360 with significant asymptotic values of unknown quantities. The steady values are examined first and then utilized in main domain to find the amplitude and oscillation in momentum-thermal transport of non-Newtonian fluid. The influence of thermal buoyancy force, radiation, magnetic field, thermophoresis and Brownian motion on the physical quantities such as velocity, streamlines, temperature, isotherms and concentration is deduced. It is noticed that the high amplitude in fluid velocity factor is depicted for high values of magnetic field, radiation and Powell-Eyring fluid parameter. Using Brownian motion and thermal buoyancy, the steady heating variation and steady nanoparticle concentration flow is better with noticeable difference. The fluctuation, oscillating frequency and phase angle of heating distribution and concentration/mass rate is increased as Schmidt factor and Prandtl coefficient increases. The concept of Powell-Eyring nanoparticles with improved theoretical and innovative mechanism is very useful in artificial heart surgery, heating-cooling of medical devices, stents coating, biodegradable magnesium stents, polymer cardio stents and other bio-medical equipment.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117054"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A reliable strategy for a category of third-kind nonlinear fractional integro-differential equations","authors":"T. Baghban ,&nbsp;M.H. Heydari ,&nbsp;M. Bayram ,&nbsp;M.A. Zaky","doi":"10.1016/j.chaos.2025.117022","DOIUrl":"10.1016/j.chaos.2025.117022","url":null,"abstract":"<div><div>This work develops a novel numerical approach for solving a class of third-kind fractional integro-differential equations, incorporating the Caputo–Hadamard derivative. To simplify the solution process, a set of piecewise basis functions, known as the piecewise shifted Jacobi polynomials, is introduced. Additionally, two closed-form expressions for the classical and Hadamard fractional integrals are derived. Furthermore, two corresponding operational matrices are constructed to enable efficient numerical computation of these integrals. In the proposed method, the fractional term of the problem is first expressed as a finite expansion in terms of the generated piecewise basis functions. Employing the derived operational matrices and exploiting the linear independence of the basis, the original equation is transformed into a system of algebraic equations, which is then solved to obtain the numerical solution. A rigorous convergence analysis is conducted, combining theoretical and numerical investigations to validate the reliability of the proposed scheme. The method is implemented on three illustrative examples, demonstrating its exceptional accuracy and computational efficiency in solving this class of fractional integro-differential equations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117022"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetry breaking for nonhomogeneous Hénon-type problems involving the 1-Laplacian operator","authors":"Marcos T.O. Pimenta ,&nbsp;Yino B. Cueva Carranza ,&nbsp;Giovany M. Figueiredo ,&nbsp;Olimpio Hiroshi Miyagaki","doi":"10.1016/j.nonrwa.2025.104480","DOIUrl":"10.1016/j.nonrwa.2025.104480","url":null,"abstract":"<div><div>In this paper we study the nonhomogeneous Hénon elliptic problem involving the 1-Laplacian operator within the unit ball. Under some assumptions on the nonlinearity, and for sufficiently large parameter values, we establish the existence of a non-radial solution. Our approach relies on an approximation scheme in which the solution is obtained as the limit of solutions to <span><math><mi>p</mi></math></span>-Laplacian type problems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104480"},"PeriodicalIF":1.8,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852257","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":"Ensuring UAV safety: A deep learning-based fault-tolerant approach with control barrier functions","authors":"Fawaz W. Alsaade ,&nbsp;Mohammed S. Al-zahrani ,&nbsp;Fuad E. Alsaadi","doi":"10.1016/j.chaos.2025.117039","DOIUrl":"10.1016/j.chaos.2025.117039","url":null,"abstract":"<div><div>Accurate control of unmanned aerial vehicles (UAVs) is vital for precise navigation and reliable execution of tasks, particularly in safety-critical scenarios. Nevertheless, actuator faults, especially rotor failures, can significantly impair UAV performance and compromise safety. This paper proposes a robust control architecture that integrates deep learning with finite-time control methods, further augmented with control barrier functions to enforce safety constraints rigorously under unknown actuator faults. A deep recurrent neural network (RNN) estimator is incorporated to identify and compensate for actuator faults in real-time. At the same time, a finite-time control mechanism ensures rapid and precise trajectory tracking. Moreover, including control barrier functions is an additional protective layer, robustly guaranteeing that the UAV remains within designated safety boundaries despite uncertainties, disturbances, and severe actuator faults. We validate the effectiveness and practicality of the proposed method using a modified five-rotor UAV model tailored for heavy-load transport tasks. Detailed finite-time stability analysis and comprehensive simulations demonstrate the practicality and enhanced performance of our proposed approach. Simulation results demonstrate superior accuracy in trajectory tracking and robust enforcement of critical safety constraints, such as maintaining a safe altitude threshold in hazardous conditions. These findings underscore the potential of the proposed framework for reliable and safe UAV operations in demanding environments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117039"},"PeriodicalIF":5.6,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global solutions to the angiogenesis system with p-Laplacian diffusion","authors":"Changchun Liu,&nbsp;Yue Zhou","doi":"10.1016/j.nonrwa.2025.104478","DOIUrl":"10.1016/j.nonrwa.2025.104478","url":null,"abstract":"<div><div>In this paper, we consider a angiogenesis system with <span><math><mi>p</mi></math></span>-Laplacian diffusion <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mrow><mo>(</mo><msup><mrow><mfenced><mrow><mo>∇</mo><mi>u</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>δ</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mi>u</mi><mo>∇</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary. For all <span><span><span><math><mrow><mi>p</mi><mo>&gt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>N</mi></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>}</mo></mrow><mo>,</mo></mrow></math></span></span></span>we prove the existence of global strong solution.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104478"},"PeriodicalIF":1.8,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858431","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}