数学最新文献

{"title":"Higher fractional differentiability for solutions to parabolic equations with double-phase growth","authors":"Lijing Zhao, Shenzhou Zheng","doi":"10.1016/j.nonrwa.2024.104270","DOIUrl":"10.1016/j.nonrwa.2024.104270","url":null,"abstract":"<div><div>We devote this paper to a higher fractional differentiability of solutions for a class of parabolic double-phase equations <span><span><span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>−</mo><mtext>div</mtext><mfenced><mrow><msup><mrow><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>D</mi><mi>u</mi><mo>+</mo><mi>a</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>D</mi><mi>u</mi></mrow></mfenced><mo>=</mo><mo>−</mo><mtext>div</mtext><mfenced><mrow><msup><mrow><mrow><mo>|</mo><mi>F</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>F</mi><mo>+</mo><mi>a</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>F</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>F</mi></mrow></mfenced><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>.</mo></mrow></math></span></span></span>A higher fractional differentiability of spatial gradients is established by way of the finite difference quotient, under assumptions that <span><math><mrow><mn>0</mn><mo>≤</mo><mi>a</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>α</mi><mo>,</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mrow><mo>(</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, the exponents <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></math></span> satisfies <span><math><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>q</mi><mo>≤</mo><mi>p</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mi>α</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mrow></math></span>, and <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> belongs to <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>l</mi><mi>o</mi><mi>c</mi></mrow><mrow><mi>ϑ</mi></mrow></msubsup><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>Φ</mi><mo>,</mo><mi>∞</mi><mo>;</mo><mi>l</mi><mi>o</mi><mi>c</mi></mrow><mrow><mspace></mspace><mi>β</mi></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mn>0</mn><mo><</mo><mi>β</mi><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>ϑ</mi><mo>≔</mo><mo>max</mo><mrow><mo>{</mo><mfrac><mrow><mi>q</mi><mrow><mo>(</mo><mn>2</mn><mi>q</mi><mo>−</mo><mi>p</mi><mo>)</mo></mro","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104270"},"PeriodicalIF":1.8,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142757322","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":"Assessing the vulnerability of empirical infrastructure networks to natural catastrophes","authors":"Tomas Scagliarini ,&nbsp;Oriol Artime ,&nbsp;Manlio De Domenico","doi":"10.1016/j.chaos.2024.115813","DOIUrl":"10.1016/j.chaos.2024.115813","url":null,"abstract":"<div><div>Human-made infrastructures are complex systems continually exposed to events that threat their function, such as cascading failures, occurring when the flow of physical quantities is redistributed within the network as a consequence of localized disruptions. Nevertheless, the role played by exogenous catastrophic events and internal failures on the robustness of critical infrastructures is usually addressed independently, under simplifying assumptions and lacking a unified picture for realistic risk assessments. Here, we fill this gap by introducing the Operational-Affected-Dismantled (<em>OAD</em>) model that captures both local and nonlocal failure propagation mechanisms. The model combines reaction–diffusion processes for local spreading with a global field effect for long-range interactions, allowing us to quantitatively characterize the cascade dynamics in infrastructure networks. Moreover, we include information on external stressors to assess the robustness of empirical network infrastructures and build spatial risk maps. By using data from severe storms (2009–2016) and from earthquakes (2000–2023) as stressors of the North American power grid and the worldwide airline transportation system, respectively, we offer a quantitative way to rank events by their potential to trigger systemic effects. By analyzing the response of the European power grid to simulated severe storms, we find that it can show high levels of systemic risk. Uncertainty in global climate and the accelerating frequency of extreme events all over the globe call for novel strategies to quantify, adapt to and mitigate systemic risk. Our framework provides a suitable starting point to assess the robustness of empirical systems in realistic and what-if scenarios.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115813"},"PeriodicalIF":5.3,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mathematical model for biological motor learning based on synaptic dynamics","authors":"Yuhao Shen ,&nbsp;Qi Yang","doi":"10.1016/j.chaos.2024.115839","DOIUrl":"10.1016/j.chaos.2024.115839","url":null,"abstract":"<div><div>We present a mathematical model to simulate the generation process of motor learning rate coefficients in human brain, focusing on neural communication through synaptic dynamics. The model consists of four major compartments, including three intraneuronal and one perceptron component. The motor learning rate coefficient is generated through biologically plausible changes in synaptic connections within the neural network, governed by the biological energy efficiency constraint. Our simulations for the first time demonstrated that the optimal motor learning rate coefficient as reported in previous research is biologically possible. We further validated the consistency, stability and robustness of the model. Additionally, we observed a distinct difference in the neural networks' structures between successful and failed motor learning processes. To achieve successful motor learning, it is essential that the interneuronal network is composed predominantly by inhibitory synaptic connections, and connections to the perceptron are primarily excitatory.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115839"},"PeriodicalIF":5.3,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744282","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":"Long-Term Existence for Perturbed Multiple Gas Balls and Their Asymptotic Behavior","authors":"Gerhard Ströhmer","doi":"10.1007/s00021-024-00912-0","DOIUrl":"10.1007/s00021-024-00912-0","url":null,"abstract":"<div><p>We consider the movement of self-gravitating gas balls consisting of viscous barotropic fluids in the neighborhood of an equilibrium state. If this state fulfills a certain stability condition, we show that the solutions exist for all time. We allow perturbations that change the angular momentum.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754292","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 semi-analytic collocation technique for solving 3D anomalous non-linear thermal conduction problem associated with the Caputo fractional derivative","authors":"Farzaneh Safari ,&nbsp;Yanjun Duan","doi":"10.1016/j.camwa.2024.11.032","DOIUrl":"10.1016/j.camwa.2024.11.032","url":null,"abstract":"<div><div>A semi-analytic numerical method is described as an efficient meshless approach for the solution of anomalous non-linear thermal conduction problems in functionally graded materials in which the model results in fractional boundary value problems. The first key feature in this scheme is the derivation and discretization of the fractional derivative at every time step. The second key feature is the trigonometric basis functions (TBFs) as the basis functions were introduced by the need for approximate solutions on boundary conditions with more flexibility in choosing collocation points. Moreover, the approximate solution of the anomalous thermal conduction problems converges to the exact solution as <em>γ</em> is closed to 1 in the full closed time interval for three simulated numerical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"178 ","pages":"Pages 81-91"},"PeriodicalIF":2.9,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747504","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":"Corrigendum to “On certain maximal hyperelliptic curves related to Chebyshev polynomials” [J. Number Theory 203 (2019) 276–293]","authors":"Saeed Tafazolian ,&nbsp;Jaap Top","doi":"10.1016/j.jnt.2024.10.011","DOIUrl":"10.1016/j.jnt.2024.10.011","url":null,"abstract":"","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 427-428"},"PeriodicalIF":0.6,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744084","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":"Nonlinear pitch oscillation and control of a gravitational stabilized sailcraft perturbed by solar pressure torque","authors":"Lu Liu ,&nbsp;Junwei Luo ,&nbsp;Weiwei Wang,&nbsp;Shuqi Gao,&nbsp;Junsheng Li,&nbsp;Jiafu Liu","doi":"10.1016/j.chaos.2024.115814","DOIUrl":"10.1016/j.chaos.2024.115814","url":null,"abstract":"<div><div>The sailcraft based space missions is deeply influenced by its attitude dynamics since the solar radiation pressure force for propellantless orbital maneuver is dependent on its orientation with respect to the sun line. Therefore, it is essential to explore the attitude motion evolution of a sailcraft and understand its attitude dynamic characteristics. To address this, nonlinear pitch dynamics of a sailcraft in an Earth orbit with a sliding mass as an attitude control actuator is focused on. Firstly, the Lagrange equation method is adopted to establish the pitch dynamics of a sailcraft subjected to the gravitational gradient torque, solar radiation pressure torque considering the Earth's occlusion of sunlight, damping torque, and the attitude control torque (this torque is generated by positioning the sliding mass at proper location). Secondly, the possible occurrence of chaotic pitch motion free of control torque is analytically predicted for the sailcraft in the circular and elliptical orbits using the Melnikov method respectively. The effectiveness of the Melnikov method is verified using various numerical methods such as phase plane, Poincaré sections, and power spectrum density. Furthermore, the influence of various parameters on the chaotic evolution is analyzed in detail. Lastly, to control the chaotic pitch motion onto the selected unstable periodic orbit obtained using the close return pairs, a sliding mode controller based on control input anti-saturation considering the position restriction of the sliding mass is developed. The effectiveness of the developed pitch chaos stabilization controller is verified by two numerical simulation cases.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115814"},"PeriodicalIF":5.3,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744279","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":"Hysteresis in a generalized Kuramoto model with a first-order approximate coupling function and inhomogeneous coupling strengths","authors":"Jae Hyung Woo ,&nbsp;Hae Seong Lee ,&nbsp;Joon-Young Moon ,&nbsp;Tae-Wook Ko","doi":"10.1016/j.chaos.2024.115770","DOIUrl":"10.1016/j.chaos.2024.115770","url":null,"abstract":"<div><div>We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a first-order approximation of general coupling functions. With the coupling function and the coupling strength inhomogeneity, each oscillator acquires an effective intrinsic frequency proportional to its individual coupling strength. This is analogous to the positive coupling strength-frequency correlation introduced explicitly or implicitly in some previous models with nonidentical oscillators that show explosive synchronization and hysteresis. Through numerical simulations and analysis using truncated Gaussian, uniform, and truncated power-law coupling strength distributions, we observe that the system can exhibit abrupt phase transitions and hysteresis. The distribution of coupling strengths significantly affects the hysteresis regions within the parameter space of the coupling function. Additionally, numerical simulations of models with weighted networks including a brain network confirm the existence of hysteresis due to the first-order approximate coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"190 ","pages":"Article 115770"},"PeriodicalIF":5.3,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743965","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":"Bifurcation and chaos in axially moving ferromagnetic thin plates with imperfections under magnetic field and line load","authors":"Mengxue Xie ,&nbsp;Yuda Hu","doi":"10.1016/j.chaos.2024.115815","DOIUrl":"10.1016/j.chaos.2024.115815","url":null,"abstract":"<div><div>This paper explores the complex dynamic behavior of axially moving ferromagnetic thin plates with initial geometric imperfection, subject to a magnetic field and a line load. The equation of motion for the imperfect plate is derived using Hamilton's variational principle, based on Kirchhoff's thin plate theory and the magnetoelastic theory of ferromagnetic materials, and discretized via the Galerkin method. When system stiffness becomes negative under specific parameters, leading to structural instability, the Melnikov method is used to predict chaos analytically and to establish the necessary conditions for its onset. Based on these predictions, a chaotic distribution map is generated in the parameter space to visualize chaotic regions. Numerical simulations are performed to produce bifurcation diagrams, maximum Lyapunov exponent plots, and system response curves, providing a dynamic analysis of the system's behavior under varying bifurcation parameters. The results indicate a complex nonlinear coupling between the plate's physical and geometric properties and the external magnetic field conditions. Variations in magnetic field intensity, axial velocity, and frequency ratio result in complex nonlinear dynamics, including bifurcations and transitions between periodic and chaotic states. This study offers critical insights into the dynamic characteristics and evolution of nonlinear systems, with significant implications for controlling and predicting chaotic vibrations in engineering applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"190 ","pages":"Article 115815"},"PeriodicalIF":5.3,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744058","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":"Full asymptotic expansion of the permeability matrix of a dilute periodic porous medium","authors":"F. Feppon","doi":"10.1016/j.jde.2024.11.029","DOIUrl":"10.1016/j.jde.2024.11.029","url":null,"abstract":"<div><div>We compute full asymptotic expansions of the permeability matrix of a laminar fluid flowing through a periodic array of small solid particles. The derivation considers obstacles with arbitrary shape in arbitrary space dimension. In the first step, we use hydrodynamics layer potential theory to obtain the asymptotic expansion of the velocity and pressure fields across the periodic array. The terms of these expansions can be computed through a procedure involving a cascade of exterior and interior problems. In the second step, we deduce the asymptotic expansion of the permeability matrix. The derivation requires evaluating Hadamard finite part integrals and tensors depending on the values of the fundamental solution or its derivatives on the faces of the unit cell. We verify that our expansions agree to the leading order with the expressions found by Hasimoto <span><span>[24]</span></span> in the case of spherical obstacles in two and three dimensions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"418 ","pages":"Pages 178-237"},"PeriodicalIF":2.4,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745975","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}