Pub Date : 2026-01-22DOI: 10.1016/j.cnsns.2026.109767
Yaojia Zhang , Tao Chen , Stanislaw Migórski
This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.
{"title":"Viscoelastic surfactant flowback model with rod-like micelle leading to differential variational-hemivariational inequality","authors":"Yaojia Zhang , Tao Chen , Stanislaw Migórski","doi":"10.1016/j.cnsns.2026.109767","DOIUrl":"10.1016/j.cnsns.2026.109767","url":null,"abstract":"<div><div>This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109767"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033540","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}
Pub Date : 2026-01-22DOI: 10.1016/j.cnsns.2026.109775
Yudong Zhou, Qinghui Zhang
Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for L2 relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.
{"title":"Extreme learning machines with decaying penalties for nonlinear partial differential equations","authors":"Yudong Zhou, Qinghui Zhang","doi":"10.1016/j.cnsns.2026.109775","DOIUrl":"10.1016/j.cnsns.2026.109775","url":null,"abstract":"<div><div>Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for <em>L</em><sup>2</sup> relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109775"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033905","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}
Pub Date : 2026-01-22DOI: 10.1016/j.cnsns.2026.109760
Xiumei Deng , Qihua Huang , Hai-Yang Jin
We develop a reaction-diffusion-taxis model to investigate the dynamic interactions between a toxicant and a predator-prey system within a contaminated aquatic ecosystem. The model includes taxis terms induced by the toxicant to capture the evasive movement of individuals as they seek to avoid exposure to the toxicant. We establish the global well-posedness of solutions for the reaction-diffusion-taxis system. We prove the global asymptotic stability of spatially uniform steady states. Through linear stability analysis, we derive sufficient conditions for the destabilization of these uniform steady states. Numerically, we explore the influence of key toxicant-related parameters—such as toxicant input rate, toxicant-taxis intensity, and species susceptibility to toxicants—on the persistence and spatial distribution of prey and predator populations. Our results demonstrate that: (i) High-intensity toxicant-taxis can induce spatial segregation and aggregation patterns between the toxicant and populations; (ii) when predators are more susceptible to toxicants than their prey, a moderate increase in toxicant concentration may, counterintuitively, enhance prey persistence; and (iii) spatially heterogeneous toxicant inputs can promote species persistence, thereby supporting ecosystem biodiversity.
{"title":"A reaction-diffusion-taxis model for toxicant-predator-prey interaction dynamics","authors":"Xiumei Deng , Qihua Huang , Hai-Yang Jin","doi":"10.1016/j.cnsns.2026.109760","DOIUrl":"10.1016/j.cnsns.2026.109760","url":null,"abstract":"<div><div>We develop a reaction-diffusion-taxis model to investigate the dynamic interactions between a toxicant and a predator-prey system within a contaminated aquatic ecosystem. The model includes taxis terms induced by the toxicant to capture the evasive movement of individuals as they seek to avoid exposure to the toxicant. We establish the global well-posedness of solutions for the reaction-diffusion-taxis system. We prove the global asymptotic stability of spatially uniform steady states. Through linear stability analysis, we derive sufficient conditions for the destabilization of these uniform steady states. Numerically, we explore the influence of key toxicant-related parameters—such as toxicant input rate, toxicant-taxis intensity, and species susceptibility to toxicants—on the persistence and spatial distribution of prey and predator populations. Our results demonstrate that: (i) High-intensity toxicant-taxis can induce spatial segregation and aggregation patterns between the toxicant and populations; (ii) when predators are more susceptible to toxicants than their prey, a moderate increase in toxicant concentration may, counterintuitively, enhance prey persistence; and (iii) spatially heterogeneous toxicant inputs can promote species persistence, thereby supporting ecosystem biodiversity.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109760"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033904","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}
Pub Date : 2026-01-21DOI: 10.1016/j.cnsns.2026.109776
Zirui Du, Tianliang Hou
In this paper, we present first- and second-order stabilized exponential-SAV (sESAV) schemes preserving energy stability and maximum bound principle (MBP) for ternary Allen-Cahn equations. We prove that the first-order sESAV (sESAV1) scheme unconditionally preserves the discrete MBP and energy stability, the second-order sESAV (sESAV2) scheme preserves energy stability unconditionally and the discrete MBP under a constraint on temporal step size τ. Optimal L∞ error estimates for sESAV1 and sESAV2 are rigorously analyzed. To the best of our knowledge, it is the first time to discuss L∞ error estimates for SAV-type schemes. Several numerical experiments are performed to verify the validity of our schemes.
{"title":"Stabilized exponential-SAV schemes preserving energy stability and maximum bound principle for ternary Allen-Cahn equations","authors":"Zirui Du, Tianliang Hou","doi":"10.1016/j.cnsns.2026.109776","DOIUrl":"10.1016/j.cnsns.2026.109776","url":null,"abstract":"<div><div>In this paper, we present first- and second-order stabilized exponential-SAV (sESAV) schemes preserving energy stability and maximum bound principle (MBP) for ternary Allen-Cahn equations. We prove that the first-order sESAV (sESAV1) scheme unconditionally preserves the discrete MBP and energy stability, the second-order sESAV (sESAV2) scheme preserves energy stability unconditionally and the discrete MBP under a constraint on temporal step size <em>τ</em>. Optimal <em>L</em><sup>∞</sup> error estimates for sESAV1 and sESAV2 are rigorously analyzed. To the best of our knowledge, it is the first time to discuss <em>L</em><sup>∞</sup> error estimates for SAV-type schemes. Several numerical experiments are performed to verify the validity of our schemes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109776"},"PeriodicalIF":3.8,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033545","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}
Pub Date : 2026-01-20DOI: 10.1016/j.cnsns.2026.109765
Roya Vaziri Doghezlou, Hamid Reza Tabrizidooz, Mostafa Shamsi
{"title":"A fully direct transcription method for solving distributed-order time-fractional diffusion optimal control problems with unilateral constraints","authors":"Roya Vaziri Doghezlou, Hamid Reza Tabrizidooz, Mostafa Shamsi","doi":"10.1016/j.cnsns.2026.109765","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109765","url":null,"abstract":"","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"180 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014795","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}
Pub Date : 2026-01-20DOI: 10.1016/j.cnsns.2026.109766
Fei Yan , Hao Wang , Yingmin Yi
This paper proposes a novel model-free adaptive control with independent time-varying parameters (MFAC-ITVP) framework for containment control in nonlinear multi-agent systems (MASs). Unlike conventional MFAC schemes that require globally homogeneous controller parameters, the proposed framework allows each agent to autonomously adjust its controller gains through independently evolving time-varying parameters. This independence significantly enhances adaptability and robustness, especially under dynamic communication topologies and varying agent participation. By transforming nonlinear agent dynamics into local data-driven linear models through dynamic linearization, a fully distributed control law is developed that depends solely on local input–output data without any prior model knowledge. Rigorous theoretical analysis establishes convergence and stability in the maximum-norm sense under generalized Lipschitz conditions. Extensive simulations under both fixed and switching topologies verify that the proposed MFAC-ITVP method achieves faster convergence and stronger disturbance rejection compared with traditional MFAC approaches.
{"title":"Model-free adaptive control with independent time-varying parameters for containment control in multi-agent systems","authors":"Fei Yan , Hao Wang , Yingmin Yi","doi":"10.1016/j.cnsns.2026.109766","DOIUrl":"10.1016/j.cnsns.2026.109766","url":null,"abstract":"<div><div>This paper proposes a novel model-free adaptive control with independent time-varying parameters (MFAC-ITVP) framework for containment control in nonlinear multi-agent systems (MASs). Unlike conventional MFAC schemes that require globally homogeneous controller parameters, the proposed framework allows each agent to autonomously adjust its controller gains through independently evolving time-varying parameters. This independence significantly enhances adaptability and robustness, especially under dynamic communication topologies and varying agent participation. By transforming nonlinear agent dynamics into local data-driven linear models through dynamic linearization, a fully distributed control law is developed that depends solely on local input–output data without any prior model knowledge. Rigorous theoretical analysis establishes convergence and stability in the maximum-norm sense under generalized Lipschitz conditions. Extensive simulations under both fixed and switching topologies verify that the proposed MFAC-ITVP method achieves faster convergence and stronger disturbance rejection compared with traditional MFAC approaches.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109766"},"PeriodicalIF":3.8,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014494","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}
Pub Date : 2026-01-19DOI: 10.1016/j.cnsns.2026.109759
Wenjie Jiang, Lingqiang Li
To address the challenge of handling complex uncertainty problems faced by single variable precision fuzzy rough set (VPFRS), this paper introduces a new model of double-parameter VPFRS and constructs a new Three-way decision (TWD) model based on it. Firstly, considering the misclassification rate parameter and the fuzzy relation cut-level parameter, we introduce a new double-parameter VPFRS model as well as its multi-granularity extension. The new model uses overlap and grouping functions as the logical value domain of fuzzy sets, which enables the model to have strong interpretability and excellent mathematical properties. In addition, the two parameters in the model can better reduce the interference of noise data, and multi-granularity can reflect multi-strategy. Secondly, we integrate the proposed multi-granularity double-parameter VPFRS model with the technique for order preference by similarity to an ideal solution (TOPSIS) method to construct a TWD with noise reduction and multi-strategy. Finally, we apply this new method to the risk assessment of pregnant health (https://archive.ics.uci.edu/dataset/863/pregnant+health+risk). The effectiveness, stability and reliability of the TWD are verified through parameter analysis, comparative experiments, ordered similarity experiment. The experimental results show that our TWD method can accurately classify 376 pregnant women in the dataset into three categories: positive class (high risk), negative class (low risk), and boundary class (medium risk), and the overall classification accuracy with overlap functions and grouping functions can reach 98.4%, which is 3.5% higher than that with traditional methods. Meanwhile, our method can rank the pregnant women according to their risk levels for disease, thereby providing a scientific basis for determining the priority order of treatment.
针对单变量精度模糊粗糙集（VPFRS）在处理复杂不确定性问题时所面临的挑战，提出了一种新的双参数模糊粗糙集模型，并在此基础上构建了一种新的三向决策（TWD）模型。首先，考虑误分类率参数和模糊关系切层参数，提出了一种新的双参数VPFRS模型及其多粒度扩展；该模型采用重叠和分组函数作为模糊集的逻辑值域，使模型具有较强的可解释性和较好的数学性质。此外，模型中的两个参数可以更好地降低噪声数据的干扰，多粒度可以体现多策略。其次，我们将所提出的多粒度双参数VPFRS模型与TOPSIS （similarity to a ideal solution）排序偏好技术相结合，构建了具有降噪和多策略的TWD模型。最后，我们将这种新方法应用于孕妇健康风险评估（https://archive.ics.uci.edu/dataset/863/pregnant+health+risk）。通过参数分析、对比实验、有序相似实验，验证了TWD的有效性、稳定性和可靠性。实验结果表明，我们的TWD方法可以准确地将数据集中的376名孕妇分为阳性类（高风险）、阴性类（低风险）和边界类（中风险）三类，具有重叠函数和分组函数的总体分类准确率可达98.4%，比传统方法提高3.5%。同时，我们的方法可以根据孕妇的疾病风险等级对其进行排序，从而为确定优先治疗顺序提供科学依据。
{"title":"A multi-strategy strong noise three-way decision originating from double-parameter multi-granularity variable precision fuzzy rough sets","authors":"Wenjie Jiang, Lingqiang Li","doi":"10.1016/j.cnsns.2026.109759","DOIUrl":"10.1016/j.cnsns.2026.109759","url":null,"abstract":"<div><div>To address the challenge of handling complex uncertainty problems faced by single variable precision fuzzy rough set (VPFRS), this paper introduces a new model of double-parameter VPFRS and constructs a new Three-way decision (TWD) model based on it. Firstly, considering the misclassification rate parameter and the fuzzy relation cut-level parameter, we introduce a new double-parameter VPFRS model as well as its multi-granularity extension. The new model uses overlap and grouping functions as the logical value domain of fuzzy sets, which enables the model to have strong interpretability and excellent mathematical properties. In addition, the two parameters in the model can better reduce the interference of noise data, and multi-granularity can reflect multi-strategy. Secondly, we integrate the proposed multi-granularity double-parameter VPFRS model with the technique for order preference by similarity to an ideal solution (TOPSIS) method to construct a TWD with noise reduction and multi-strategy. Finally, we apply this new method to the risk assessment of pregnant health (<span><span>https://archive.ics.uci.edu/dataset/863/pregnant+health+risk</span><svg><path></path></svg></span>). The effectiveness, stability and reliability of the TWD are verified through parameter analysis, comparative experiments, ordered similarity experiment. The experimental results show that our TWD method can accurately classify 376 pregnant women in the dataset into three categories: positive class (high risk), negative class (low risk), and boundary class (medium risk), and the overall classification accuracy with overlap functions and grouping functions can reach 98.4%, which is 3.5% higher than that with traditional methods. Meanwhile, our method can rank the pregnant women according to their risk levels for disease, thereby providing a scientific basis for determining the priority order of treatment.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109759"},"PeriodicalIF":3.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000863","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}
Pub Date : 2026-01-19DOI: 10.1016/j.cnsns.2026.109762
Qiuhui Yan, Xufeng Xiao, Xinlong Feng
To address the numerical oscillations encountered when solving stationary convection-dominated diffusion equations on curved surfaces using the traditional finite element method, this paper adopts a stabilized surface finite element method. This method is constructed based on the variational multiscale method with bubble functions. By introducing a two-local Gaussian integration strategy, the method effectively reduces the computational complexity of the traditional variational multiscale method. On this basis, this paper establishes a numerical framework for surface multiscale problems that balances both stability and computational efficiency. The paper conducts theoretical finite element analysis and performs numerical experiments on various curved surfaces to verify the advantages of the proposed method. Compared with the streamline diffusion method and the edge stabilization method, this method features simplicity in form and ease of analysis. While achieving stabilization effects, it can also reach the same level of accuracy as the traditional finite element method.
{"title":"A bubble-function-based variational multiscale method with two-local Gaussian integration for stationary convection-dominated diffusion equations on surfaces","authors":"Qiuhui Yan, Xufeng Xiao, Xinlong Feng","doi":"10.1016/j.cnsns.2026.109762","DOIUrl":"10.1016/j.cnsns.2026.109762","url":null,"abstract":"<div><div>To address the numerical oscillations encountered when solving stationary convection-dominated diffusion equations on curved surfaces using the traditional finite element method, this paper adopts a stabilized surface finite element method. This method is constructed based on the variational multiscale method with bubble functions. By introducing a two-local Gaussian integration strategy, the method effectively reduces the computational complexity of the traditional variational multiscale method. On this basis, this paper establishes a numerical framework for surface multiscale problems that balances both stability and computational efficiency. The paper conducts theoretical finite element analysis and performs numerical experiments on various curved surfaces to verify the advantages of the proposed method. Compared with the streamline diffusion method and the edge stabilization method, this method features simplicity in form and ease of analysis. While achieving stabilization effects, it can also reach the same level of accuracy as the traditional finite element method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109762"},"PeriodicalIF":3.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000860","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}
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the initial density distribution are considered: spherical and cylindrical. It is shown that the relativistic effect delays the onset of the shock wave moment, and in some cases removes it entirely or, conversely, can facilitate it.
The analysis of the system's dynamics is carried out within the Wigner-Vlasov formalism, which makes it possible to extend the obtained solutions to quantum systems, including those with gravitational interaction. The derived exact solutions can be directly used as a cross-check for modeling and optimizing nonlinear problems of beam dynamics with account for space charge, astrophysics, plasma physics, and quantum systems with a shock wave.
{"title":"Exact solutions for the relativistic dynamics of a self-consistent problem for system with electromagnetic and gravitational interaction within the Wigner-Vlasov formalism","authors":"E.E. Perepelkin , B.I. Sadovnikov , N.G. Inozemtseva , I.Yu. Baibara","doi":"10.1016/j.cnsns.2026.109761","DOIUrl":"10.1016/j.cnsns.2026.109761","url":null,"abstract":"<div><div>This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the initial density distribution are considered: spherical and cylindrical. It is shown that the relativistic effect delays the onset of the shock wave moment, and in some cases removes it entirely or, conversely, can facilitate it.</div><div>The analysis of the system's dynamics is carried out within the Wigner-Vlasov formalism, which makes it possible to extend the obtained solutions to quantum systems, including those with gravitational interaction. The derived exact solutions can be directly used as a cross-check for modeling and optimizing nonlinear problems of beam dynamics with account for space charge, astrophysics, plasma physics, and quantum systems with a shock wave.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109761"},"PeriodicalIF":3.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000861","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}
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