Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Existence and continuity of pullback exponential attractors for a family of non-classical reaction-diffusion equations","authors":"Vinicius Tavares Azevedo ,&nbsp;Heraclio López-Lázaro ,&nbsp;Carlos R. Takaessu Junior","doi":"10.1016/j.cnsns.2025.109198","DOIUrl":"10.1016/j.cnsns.2025.109198","url":null,"abstract":"<div><div>In this work, we investigate the pullback asymptotic behavior of a family of semilinear reaction-diffusion evolution equations with non-autonomous parameters <span><math><msub><mrow><mo>{</mo><msub><mi>γ</mi><mi>ϵ</mi></msub><mrow><mo>(</mo><mo>·</mo><mo>)</mo></mrow><mo>}</mo></mrow><mrow><mrow><mi>ε</mi></mrow><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></msub></math></span> located in the non-classical term. Under suitable growth and dissipativity conditions, we prove the existence and stability of a family of pullback exponential attractors associated with our problem. As a consequence of the technique applied, we obtain that the sections of the family of the pullback attractors, which existence was proved by Rivero [1], possess uniformly finite fractal dimension with respect to <span><math><mrow><mi>ϵ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. Such improvement is possible by performing a change of variables in the equations, which allows us to transfer our analysis from <span><math><mrow><msubsup><mi>H</mi><mn>0</mn><mn>1</mn></msubsup><mrow><mo>(</mo><mstyle><mi>Ω</mi></mstyle><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mstyle><mi>Ω</mi></mstyle><mo>)</mo></mrow></mrow></math></span>. This change of spaces is the key to obtaining the necessary embedding to establish the smoothing property (see [2, Theorem 2.5] or [3]), overcoming the difficulties present in the original problem. Finally, we establish the continuity of this family of pullback exponential attractors and show the upper semicontinuity of the family of pullback attractors.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109198"},"PeriodicalIF":3.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826315","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":"Energy dissipation laws and optimal convergence analysis of a transformed L1 scheme for a time-fractional Allen-Cahn equation","authors":"Zeyu Ding ,&nbsp;Na An ,&nbsp;Chaobao Huang","doi":"10.1016/j.cnsns.2025.109200","DOIUrl":"10.1016/j.cnsns.2025.109200","url":null,"abstract":"<div><div>This paper considers the two-dimensional time-fractional Allen-Cahn equation with the double-well potential <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo>(</mo><msup><mi>u</mi><mn>2</mn></msup><mo>−</mo><mi>u</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>/</mo><mn>4</mn></mrow></math></span>, whose solutions behave a weak singularity at initial time <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Firstly, the maximum bound principle of this problem is developed. By using the transformed L1 scheme on uniform temporal meshes and the finite difference method on uniform spatial meshes, a fully-discrete scheme is constructed for the initial-boundary value problem. Furthermore, the discrete maximum bound principle for the proposed scheme is investigated. By means of the discrete orthogonal convolution kernels and discrete complementary convolution kernels, we demonstrate that this fully-discrete scheme preserves an energy dissipation law. Moreover, the optimal convergence analysis of the proposed scheme is established. Finally, numerical experiments are conducted to illustrate our theoretical analysis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109200"},"PeriodicalIF":3.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826316","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":"Random dynamics of 3D stochastic retarded MHD-Voight equations driven by operator type noise","authors":"Qiangheng Zhang ,&nbsp;Mirelson M. Freitas","doi":"10.1016/j.cnsns.2025.109204","DOIUrl":"10.1016/j.cnsns.2025.109204","url":null,"abstract":"<div><div>In this paper, we study the existence, uniqueness and topological properties of pullback random attractors for the non-autonomous stochastic magnetohydrodynamics (MHD)-Voight equation with delays driven by operator type noise. First, we prove the existence, uniqueness and forward compactness of pullback random attractors. Second, we investigate the upper semi-continuity of pullback random attractors as the delay time tends to zero. Third, we consider the upper semi-continuity of pullback random attractors as the strength of noise approaches to zero. Finally, we show that the asymptotic autonomy of pullback random attractors as the time parameter goes to positive infinity. Since the solution of this equation has no higher regularity, we use the spectrum decomposition technique to prove the asymptotic compactness of the solution operator. It seems that this is the first time to study the random dynamics of the non-autonomous stochastic MHD-Voight equation with delays driven by Laplace-multiplier noise.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109204"},"PeriodicalIF":3.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827986","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":"Physics-informed fractional machine intelligence and space–time wavelet frameworks for non-local integro-partial differential equations involving weak singularities","authors":"Sudarshan Santra,&nbsp;Ratikanta Behera","doi":"10.1016/j.cnsns.2025.109184","DOIUrl":"10.1016/j.cnsns.2025.109184","url":null,"abstract":"<div><div>This paper presents a space–time multi-dimensional wavelet framework and a physics-informed fractional machine intelligence (PI-fMI) model to address the weak singularity involved in time-fractional integro-partial differential equations with mixed Volterra–Fredholm operators. Conventional machine learning approaches often struggle with weak initial singularities; however, our proposed approach overcomes this challenge through two complementary strategies in the context of fractional-order integro-differential equations. First, a wavelet-based numerical scheme is employed that utilizes the multi-resolution analysis with the collocation method to compute the wavelet coefficients, ensuring convergence for fractional-order integro-differential problems with sufficiently smooth solutions. Second, we introduce a PI-fMI model for problems that exhibit unbounded temporal derivatives at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>, which incorporates the <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> discretization for fractional operators, a combination of the repeated quadrature rule, and automatic differentiation to handle integral operators that contain diffusion terms. Theoretical and numerical analyses demonstrate that the proposed approach successfully resolves the initial weak singularities where the traditional Haar wavelets fail to address such issues. Furthermore, the convergence of the PI-fMI model is analyzed for problems with nonlinear source terms, demonstrating its effectiveness under suitable hyperparameter choices. Theoretical findings are validated through extensive numerical experiments on several test problems exhibiting bounded and unbounded temporal derivatives at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109184"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780856","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":"The parareal algorithm based on a new local time-integrator for nonlinear Caputo–Hadamard fractional differential equations","authors":"Tingting He ,&nbsp;Tianle Zhai ,&nbsp;Xuhang Huang ,&nbsp;Min Li","doi":"10.1016/j.cnsns.2025.109183","DOIUrl":"10.1016/j.cnsns.2025.109183","url":null,"abstract":"<div><div>This paper introduces a novel parareal algorithm for solving nonlinear Caputo–Hadamard fractional differential equations. Due to the nonlocal nature of fractional Hadamard derivatives and integrals, conventional parareal algorithms cannot be directly applied. To address this issue, we first localize the Hadamard derivative using the Adaptive Antoulas–Anderson (AAA) algorithm, which helps to construct local time integrators. We design a parareal algorithm based on this localization, employing a one-step scheme. We establish the convergence of the algorithm and provide numerical experiments demonstrating that it outperforms the parareal algorithm using a local time integrator based on sum-of-exponentials approximation under certain conditions. Additionally, the proposed local time integrator reduces the matrix dimensionality in the one-step scheme, offering a computational advantage over using the local time integrator based on sum-of-exponentials approximation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109183"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780858","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 gauge-Uzawa finite element method for the incompressible vector potential magnetohydrodynamics system","authors":"Zhiyong Si,&nbsp;Shengguang Chen,&nbsp;Yunxia Wang","doi":"10.1016/j.cnsns.2025.109199","DOIUrl":"10.1016/j.cnsns.2025.109199","url":null,"abstract":"<div><div>This paper considers the gauge-Uzawa finite element method(GU-FEM) for the three -dimensional incompressible magnetohydrodynamics system based on the magnetic vector potential formulation, where <span><math><mrow><mi>B</mi><mo>=</mo><mi>curl</mi><mi>A</mi></mrow></math></span>, and <span><math><mi>A</mi></math></span> is the magnetic potential. The proposed method constitutes a fully discrete projection framework that synergizes the merits of canonical and Uzawa-type formulations while maintaining variational consistency. This method is used to ensure the numerical consistency between different physical quantities when solving partial differential equations, thereby improving calculation accuracy and stability. Under specific assumptions, unconditional stability is established, along with error estimates for the velocity, pressure, and magnetic potential. The effectiveness of the guage-Uzawa finite element method is verified by numerical experiments.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109199"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827987","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":"Space-time marching-based neural direct method for the high-dimensional Hamilton-Jacobi-Bellman equation","authors":"Xiangyu Zhang ,&nbsp;Faguo Wu ,&nbsp;Xiao Zhang","doi":"10.1016/j.cnsns.2025.109196","DOIUrl":"10.1016/j.cnsns.2025.109196","url":null,"abstract":"<div><div>The Hamilton-Jacobi-Bellman (HJB) equation is a fundamental partial differential equation (PDE) in optimal control theory, but solving it in a high-dimensional space presents severe challenges due to the curse of dimensionality (CoD). Recently, a class of methods that combine neural networks with traditional direct methods, referred to here as neural direct methods, has achieved success in the numerical solution of the high-dimensional HJB equation. Nevertheless, existing neural direct methods struggle with convergence when applied to the HJB equation with a long time horizon. A similar issue also arises when the effective solution domains of these methods are expanded. Through theoretical analysis, we identify one underlying cause of these issues as the exponential propagation of nonlinearity in the state dynamics over time, which significantly increases the difficulty of solving long-horizon problems. To address these challenges, we propose a space-time marching-based neural direct method (STM-NDM), which solves the HJB equation with gradually increasing difficulty levels. For each level, the HJB equation is recast as an optimal feedback control problem that accounts for midway disturbances, which is solved by a modified direct single shooting (DSS) method with neural network parameterization. Experimental results on several high-dimensional HJB equations corresponding to path planning problems validate the effectiveness of the STM-NDM.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109196"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861021","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":"Non-isothermal hydrodynamic modeling and analysis for the flow boiling in microchannels based heat exchanger","authors":"Jingjie Cheng ,&nbsp;Qing Xia ,&nbsp;Junseok Kim ,&nbsp;Yibao Li","doi":"10.1016/j.cnsns.2025.109181","DOIUrl":"10.1016/j.cnsns.2025.109181","url":null,"abstract":"<div><div>In order to investigate the interfacial transport phenomena and the dynamics of two-phase flow in complex microchannel-based heat exchangers using phase field theory, a non-isothermal hydrodynamic model is formulated for quasi-incompressible binary fluids. We present the governing equations rigorously, which is composed of Cahn–Hilliard equations, quasi-incompressible Navier–Stokes equations and an energy equation. In order to prove the second law of thermodynamics and energy conservation law, strict theoretical system has been established. This system is an upgrade and modification for previous models in dealing with interfacial problems. By deriving the semi-discrete numerical schemes in time using the Crank–Nicolson method, we get a new algorithm efficiently and stably. The second law of thermodynamics and energy conservation law are also proved to be valid in numerical schemes. A series of numerical experiments have been conducted to demonstrate the stability and robustness of our algorithm.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109181"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772759","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":"Dispersion characteristics of solute transport in porous channel flow with uniform vertical cross-flow","authors":"Sourav Hossain ,&nbsp;Swarup Barik ,&nbsp;Christina W. Tsai","doi":"10.1016/j.cnsns.2025.109195","DOIUrl":"10.1016/j.cnsns.2025.109195","url":null,"abstract":"<div><div>The primary goal of the present work is to analytically examine the two-dimensional (2D) solute concentration distribution in an incompressible viscous fluid flow subjected to uniform vertical cross-flow. The system consists of parallel plates filled with an isotropic porous medium, with boundary adsorption at the bottom plate. Mei’s homogenization technique has been used to obtain the analytical solution for the proposed model. The analysis explores the effects of cross-flow strength on the axial velocity profile, dispersion coefficient, and mean and transverse concentration distributions while accounting for porosity in the channel. Results reveal that cross-flow significantly reduces solute concentration near the top plate, causes aggregation near the bottom plate, and leads to a slower decrease at the channel centerline. These effects become more pronounced with increasing cross-flow intensity. The dispersion coefficient shows a complex dependence on the cross-flow Peclet number <span><math><mrow><mi>P</mi><msub><mi>e</mi><mi>v</mi></msub></mrow></math></span>, exhibiting both monotonic and non-monotonic behaviors. Additionally, the influence of the Darcy number and wall adsorption on solute transport dynamics under cross-flow conditions is examined. For small Darcy numbers (<span><math><mrow><mi>D</mi><mi>a</mi><mo>≪</mo><mn>1</mn></mrow></math></span>), Taylor dispersivity decreases significantly for any fixed <span><math><msub><mrow><mi>P</mi><mi>e</mi></mrow><mi>v</mi></msub></math></span>. When wall adsorption is active, solute aggregation near the bottom plate is reduced, although a high-concentration zone still persists near the lower boundary. These findings provide valuable insights into solute dispersion under cross-flow conditions, with implications for cross-flow filtration and various chemical and biomedical applications where cross-flow plays a critical role. The novelty of this work lies in the application of a multi-scale homogenization approach to analyze dispersion phenomena within a parallel plate porous channel under vertical cross-flow, while simultaneously accounting for wall adsorption effects and enabling the coupled evaluation of mean and transverse concentration profiles.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109195"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861023","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":"Cooperative emergence induced by asymmetric punishment and strategy persistence mechanisms in multilayer networks","authors":"Yuping Li ,&nbsp;Wensheng Jia ,&nbsp;Luping Liu","doi":"10.1016/j.cnsns.2025.109187","DOIUrl":"10.1016/j.cnsns.2025.109187","url":null,"abstract":"<div><div>The evolution of cooperation in multilayer networks is a significant topic in complex network science, particularly regarding the effective promotion and sustainability of cooperative behaviors. Although punishment has been shown to promote cooperation, its effects are often limited without additional mechanisms to reinforce and sustain cooperative behavior. Furthermore, the majority of existing studies have concentrated on single-layer networks, thereby neglecting the complexities introduced by multilayer structures. In this paper, we investigate the impact of asymmetric punishment on the evolution of cooperation in conjunction with a strategy persistence mechanism within multilayer networks. Our results indicate that moderate coupling strength and effective asymmetric punishment can significantly enhance cooperation levels. The strategy persistence mechanism allows individuals to maintain their strategies for a defined period, thereby counteracting the negative effects of antisocial punishment and reinforcing the persistence of cooperative strategies within the network. Through the analysis presented in this paper, we aim to contribute to a deeper understanding of the emergence and stabilization of cooperation in more complex real-world scenarios.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109187"},"PeriodicalIF":3.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780855","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}