Pub Date : 2026-07-01Epub Date: 2026-01-22DOI: 10.1016/j.cnsns.2026.109670
Yanjiao Wang, Zhaogui Cai, Muqing Deng
Deep neural networks (DNNs) have the capability to describe complex nonlinear dynamics, which have aroused wide concerns. However, the existing parameter optimization methods in DNNs based on gradient suffer from the limitations of easily falling into local minima and the poor modeling results. To overcome these problems, this paper proposes a mini-batch gradient descent algorithm with dynamical moving window data and constructs a novel deep neural network architecture by using the simpler deep learning network instead of selecting weights through regulation and optimizing its parameters through the dynamical moving window based algorithm. The results of simulation experiments show that the proposed methods have better performance in accuracy and convergence rate compared with the existing methods for identifying nonlinear systems.
{"title":"A novel deep neural network with the dynamical moving window data for nonlinear system identification","authors":"Yanjiao Wang, Zhaogui Cai, Muqing Deng","doi":"10.1016/j.cnsns.2026.109670","DOIUrl":"10.1016/j.cnsns.2026.109670","url":null,"abstract":"<div><div>Deep neural networks (DNNs) have the capability to describe complex nonlinear dynamics, which have aroused wide concerns. However, the existing parameter optimization methods in DNNs based on gradient suffer from the limitations of easily falling into local minima and the poor modeling results. To overcome these problems, this paper proposes a mini-batch gradient descent algorithm with dynamical moving window data and constructs a novel deep neural network architecture by using the simpler deep learning network instead of selecting weights through regulation and optimizing its parameters through the dynamical moving window based algorithm. The results of simulation experiments show that the proposed methods have better performance in accuracy and convergence rate compared with the existing methods for identifying nonlinear systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109670"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033543","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 : 2026-07-01Epub Date: 2026-02-02DOI: 10.1016/j.cnsns.2026.109814
Qi Zhou , Zhigui Lin , Carlos Alberto Santos
In the transmission of faecal-oral diseases, the infected area does not always expand outward continuously. To model this phenomenon under pulse interventions, this paper proposes a free boundary problem. Our free boundary condition is governed by a nonlocal integro-differential equation, which encompasses the classical Stefan condition as a special case. First, we establish the well-posedness of the proposed problem using parabolic regularity and the contraction mapping principle. We then provide sufficient conditions for vanishing, balancing, or spreading. Finally, three numerical examples validate the theoretical results and demonstrate that this model generates more complex and realistic spatiotemporal dynamics compared to models employing the classical Stefan condition.
{"title":"Vanishing, balancing and spreading for an impulsive faecal-oral model","authors":"Qi Zhou , Zhigui Lin , Carlos Alberto Santos","doi":"10.1016/j.cnsns.2026.109814","DOIUrl":"10.1016/j.cnsns.2026.109814","url":null,"abstract":"<div><div>In the transmission of faecal-oral diseases, the infected area does not always expand outward continuously. To model this phenomenon under pulse interventions, this paper proposes a free boundary problem. Our free boundary condition is governed by a nonlocal integro-differential equation, which encompasses the classical Stefan condition as a special case. First, we establish the well-posedness of the proposed problem using parabolic regularity and the contraction mapping principle. We then provide sufficient conditions for vanishing, balancing, or spreading. Finally, three numerical examples validate the theoretical results and demonstrate that this model generates more complex and realistic spatiotemporal dynamics compared to models employing the classical Stefan condition.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109814"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110509","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 : 2026-07-01Epub Date: 2026-01-27DOI: 10.1016/j.cnsns.2026.109798
Yuanyuan Liu, Seifu Neda Tereda, Zhexin Wen
This article presents a stochastic tritrophic food chain model integrating fear-induced behavioral changes and Markov regime switching to capture environmental variability. We prove the existence of a unique global positive solution and derive a threshold condition, based on stochastic boundary processes, that governs the persistence or extinction of species under random perturbations. Our theoretical results are further supported by numerical simulations conducted using the tamed Milstein method, which overcomes the limitations of standard schemes. The findings offer valuable insights for ecological modeling, demonstrating that incorporating behavioral responses and stochasticity can have a significant impact on species dynamics.
{"title":"Dynamics of fear effect on a stochastic tritrophic level food chain model with Markov switching","authors":"Yuanyuan Liu, Seifu Neda Tereda, Zhexin Wen","doi":"10.1016/j.cnsns.2026.109798","DOIUrl":"10.1016/j.cnsns.2026.109798","url":null,"abstract":"<div><div>This article presents a stochastic tritrophic food chain model integrating fear-induced behavioral changes and Markov regime switching to capture environmental variability. We prove the existence of a unique global positive solution and derive a threshold condition, based on stochastic boundary processes, that governs the persistence or extinction of species under random perturbations. Our theoretical results are further supported by numerical simulations conducted using the tamed Milstein method, which overcomes the limitations of standard schemes. The findings offer valuable insights for ecological modeling, demonstrating that incorporating behavioral responses and stochasticity can have a significant impact on species dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109798"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071521","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 : 2026-07-01Epub Date: 2026-01-28DOI: 10.1016/j.cnsns.2026.109796
Ulises Chialva , Walter Reartes
We study the control of chaotic dynamics in the hybrid Nakano-Saito oscillator through periodic resetting schemes. In contrast to most existing approaches, which rely on Lyapunov-based constructions or optimization-driven control strategies, we focus on the underlying dynamical mechanisms responsible for the emergence of controlled and uncontrolled regimes. By analyzing the associated impact (return) map, we identify well-defined control windows that give rise to stable periodic solutions and investigate their dependence on the ratio γ between the oscillator’s natural frequency and the control frequency. We provide an analytical proof for the existence of a limit cycle and use this result to characterize the main control windows of the system, revealing distinct bifurcation phenomena that enable different regimes of chaos control within this canonical hybrid framework. Finally, we examine a stochastic resetting protocol governed by an inverse Gaussian distribution and show that it can outperform deterministic control schemes subject to timing jitter, achieving enhanced stabilization. These results demonstrate that classical dynamical systems tools are sufficient to derive precise control conditions and to assess control effectiveness even in stochastic hybrid settings.
{"title":"Chaos control and stabilization of a hybrid chaotic oscillator through deterministic and stochastic resets","authors":"Ulises Chialva , Walter Reartes","doi":"10.1016/j.cnsns.2026.109796","DOIUrl":"10.1016/j.cnsns.2026.109796","url":null,"abstract":"<div><div>We study the control of chaotic dynamics in the hybrid Nakano-Saito oscillator through periodic resetting schemes. In contrast to most existing approaches, which rely on Lyapunov-based constructions or optimization-driven control strategies, we focus on the underlying dynamical mechanisms responsible for the emergence of controlled and uncontrolled regimes. By analyzing the associated impact (return) map, we identify well-defined control windows that give rise to stable periodic solutions and investigate their dependence on the ratio <em>γ</em> between the oscillator’s natural frequency and the control frequency. We provide an analytical proof for the existence of a limit cycle and use this result to characterize the main control windows of the system, revealing distinct bifurcation phenomena that enable different regimes of chaos control within this canonical hybrid framework. Finally, we examine a stochastic resetting protocol governed by an inverse Gaussian distribution and show that it can outperform deterministic control schemes subject to timing jitter, achieving enhanced stabilization. These results demonstrate that classical dynamical systems tools are sufficient to derive precise control conditions and to assess control effectiveness even in stochastic hybrid settings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109796"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071595","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 : 2026-07-01Epub Date: 2026-01-24DOI: 10.1016/j.cnsns.2026.109790
Aiswarya Thekkeettil, Srijanani Anurag Prasad
This paper presents the construction of a hidden variable fractal interpolation function using Edelstein contractions in an iterated function system based on a finite collection of data points. The approach incorporates an iterated function system where variable functions act as vertical scaling factors leading to a generalised vector-valued fractal interpolation function. Furthermore, the paper rigorously examines the smoothness of the constructed function and establishes an upper bound for the box-counting dimension of its graph.
{"title":"Construction and box-counting dimension of the Edelstein hidden variable fractal interpolation function","authors":"Aiswarya Thekkeettil, Srijanani Anurag Prasad","doi":"10.1016/j.cnsns.2026.109790","DOIUrl":"10.1016/j.cnsns.2026.109790","url":null,"abstract":"<div><div>This paper presents the construction of a hidden variable fractal interpolation function using Edelstein contractions in an iterated function system based on a finite collection of data points. The approach incorporates an iterated function system where variable functions act as vertical scaling factors leading to a generalised vector-valued fractal interpolation function. Furthermore, the paper rigorously examines the smoothness of the constructed function and establishes an upper bound for the box-counting dimension of its graph.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109790"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047905","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 : 2026-07-01Epub Date: 2026-02-02DOI: 10.1016/j.cnsns.2026.109811
Vasily N. Govorukhin, Vyacheslav G. Tsybulin
We examine nonlinear dynamical systems that possess curves of equilibria with a changing spectrum of stability along the curve. Nontrivial cosymmetry implies the existence of these invariant objects, characterised by hidden parameters. We analyse analytically and numerically fourth- and sixth-order Galerkin models of Darcy–Lapwood convection that were previously unstudied. Bifurcations of curves of equilibria corresponding to families of convective steady-states are continued along a single physical parameter, the Rayleigh number. Our analysis reveals bifurcation scenarios that involve the birth and death of two-parameter families (hyperplanes) and one-parameter curves of equilibria. We also investigate how the stability spectrum varies due to bifurcations as the cosymmetric hidden parameter changes. Furthermore, we observe topological changes in the phase space structures, including the emergence and destruction of closed equilibrium curves. The systems under consideration demonstrate intriguing bifurcation scenarios and extend knowledge of the variety and intricacy of nonlinear phenomena in dynamical systems.
{"title":"Bifurcation phenomena in dynamical systems with a cosymmetric hidden parameter","authors":"Vasily N. Govorukhin, Vyacheslav G. Tsybulin","doi":"10.1016/j.cnsns.2026.109811","DOIUrl":"10.1016/j.cnsns.2026.109811","url":null,"abstract":"<div><div>We examine nonlinear dynamical systems that possess curves of equilibria with a changing spectrum of stability along the curve. Nontrivial cosymmetry implies the existence of these invariant objects, characterised by hidden parameters. We analyse analytically and numerically fourth- and sixth-order Galerkin models of Darcy–Lapwood convection that were previously unstudied. Bifurcations of curves of equilibria corresponding to families of convective steady-states are continued along a single physical parameter, the Rayleigh number. Our analysis reveals bifurcation scenarios that involve the birth and death of two-parameter families (hyperplanes) and one-parameter curves of equilibria. We also investigate how the stability spectrum varies due to bifurcations as the cosymmetric hidden parameter changes. Furthermore, we observe topological changes in the phase space structures, including the emergence and destruction of closed equilibrium curves. The systems under consideration demonstrate intriguing bifurcation scenarios and extend knowledge of the variety and intricacy of nonlinear phenomena in dynamical systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109811"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110508","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 : 2026-07-01Epub Date: 2026-02-07DOI: 10.1016/j.cnsns.2026.109818
Xin He , Nan-Jing Huang , Ya-Ping Fang
The alternating direction method of multipliers (ADMM) has been widely used for solving separable convex optimization problems. In this paper, by incorporating Nesterov-type extrapolation techniques, we propose two accelerated linearized ADMM schemes for two-block linearly constrained separable convex optimization problems, where each block of the objective function admits a composite structure consisting of a nonsmooth term and a smooth term. The proposed accelerated linearized ADMMs extend two classical Nesterov acceleration methods originally developed for unconstrained composite optimization to the linearly constrained setting. Under the assumption that one block of the objective function is strongly convex and that the gradients of the smooth components are Lipschitz continuous, we establish non-ergodic convergence rates of . Moreover, we show that the proposed methods reduce to accelerated linearized augmented Lagrangian methods (ALMs) when applied to one-block linearly constrained convex optimization problems. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed algorithms.
{"title":"Accelerated linearized alternating direction method of multipliers with Nesterov extrapolation","authors":"Xin He , Nan-Jing Huang , Ya-Ping Fang","doi":"10.1016/j.cnsns.2026.109818","DOIUrl":"10.1016/j.cnsns.2026.109818","url":null,"abstract":"<div><div>The alternating direction method of multipliers (ADMM) has been widely used for solving separable convex optimization problems. In this paper, by incorporating Nesterov-type extrapolation techniques, we propose two accelerated linearized ADMM schemes for two-block linearly constrained separable convex optimization problems, where each block of the objective function admits a composite structure consisting of a nonsmooth term and a smooth term. The proposed accelerated linearized ADMMs extend two classical Nesterov acceleration methods originally developed for unconstrained composite optimization to the linearly constrained setting. Under the assumption that one block of the objective function is strongly convex and that the gradients of the smooth components are Lipschitz continuous, we establish non-ergodic convergence rates of <span><math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msup><mi>k</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span>. Moreover, we show that the proposed methods reduce to accelerated linearized augmented Lagrangian methods (ALMs) when applied to one-block linearly constrained convex optimization problems. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed algorithms.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109818"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134761","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 : 2026-07-01Epub Date: 2026-01-23DOI: 10.1016/j.cnsns.2026.109786
Jinhong Jia , Chuanting Jiang , Yiqun Li , Mengmeng Liu , Wenlin Qiu
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the well-posedness of the model as well as its high order regularity estimates. To accommodate the convolution term in the reformulated model, we adopt the Ritz-Volterra finite element projection and then derive the rigorous error estimate for the fully-discretized finite element scheme. To circumvent the high computational cost from the temporal integral term, we exploit the translational invariance of the discrete coefficients associated with the convolution structure and construct a fast divide-and-conquer algorithm which reduces the computational complexity from O(MN2) to O(MNln 2N). Numerical experiments are provided to verify the theoretical results and to demonstrate the accuracy and efficiency of the proposed method.
{"title":"Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm","authors":"Jinhong Jia , Chuanting Jiang , Yiqun Li , Mengmeng Liu , Wenlin Qiu","doi":"10.1016/j.cnsns.2026.109786","DOIUrl":"10.1016/j.cnsns.2026.109786","url":null,"abstract":"<div><div>We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the well-posedness of the model as well as its high order regularity estimates. To accommodate the convolution term in the reformulated model, we adopt the Ritz-Volterra finite element projection and then derive the rigorous error estimate for the fully-discretized finite element scheme. To circumvent the high computational cost from the temporal integral term, we exploit the translational invariance of the discrete coefficients associated with the convolution structure and construct a fast divide-and-conquer algorithm which reduces the computational complexity from <em>O</em>(<em>MN</em><sup>2</sup>) to <em>O</em>(<em>MN</em>ln <sup>2</sup><em>N</em>). Numerical experiments are provided to verify the theoretical results and to demonstrate the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109786"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033536","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 : 2026-07-01Epub Date: 2026-01-31DOI: 10.1016/j.cnsns.2026.109804
Yanjun Zhao , Haibin Sun , Linlin Hou , Dong Yang
The study explores a fully distributed secure bipartite containment control strategy utilizing a dynamic event-triggered mechanism (ETM) for multi-agent systems (MASs). The MASs are susceptible to Denial-of-Service (DoS) attacks at the network layer, sensor faults, and external disturbances at the physical layer. An intermediate variable-assisted observer is devised to estimate both the unknown system states and sensor faults concurrently. Furthermore, a decentralized disturbance observer is introduced to estimate the unknown external disturbances. Subsequently, a fully distributed secure control approach is formulated to enable the system to achieve bipartite containment control goals, even under the presence of an insecure network and adverse physical conditions. Moreover, a dynamic ETM is incorporated to optimize the utilization of communication resources, with a rigorous proof of its Zeno-free property. Finally, a simulation involving unmanned marine vehicles (UMVs) is conducted to validate the efficacy of the devised methodology.
{"title":"Fully distributed secure bipartite containment control for multi-agent systems under sensor faults and external disturbances: Application to UMVs","authors":"Yanjun Zhao , Haibin Sun , Linlin Hou , Dong Yang","doi":"10.1016/j.cnsns.2026.109804","DOIUrl":"10.1016/j.cnsns.2026.109804","url":null,"abstract":"<div><div>The study explores a fully distributed secure bipartite containment control strategy utilizing a dynamic event-triggered mechanism (ETM) for multi-agent systems (MASs). The MASs are susceptible to Denial-of-Service (DoS) attacks at the network layer, sensor faults, and external disturbances at the physical layer. An intermediate variable-assisted observer is devised to estimate both the unknown system states and sensor faults concurrently. Furthermore, a decentralized disturbance observer is introduced to estimate the unknown external disturbances. Subsequently, a fully distributed secure control approach is formulated to enable the system to achieve bipartite containment control goals, even under the presence of an insecure network and adverse physical conditions. Moreover, a dynamic ETM is incorporated to optimize the utilization of communication resources, with a rigorous proof of its Zeno-free property. Finally, a simulation involving unmanned marine vehicles (UMVs) is conducted to validate the efficacy of the devised methodology.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109804"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095739","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 : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.cnsns.2026.109801
Yinting Liu , Housen Wang , Qiang Liu
This paper is concerned with the nonexistence of nontrivial global weak solutions for a class of strongly damped wave equations, involving the p-Laplacian term and combined nonlinearities. Employing the test function method, we establish rigorous conditions on the initial data and some exponents that ensure that solutions cannot exist globally in time. In addition, we give an upper bound of lifespan time of the solution. Our results reveal how the strong damping term influences the competition between the p-Laplace operator and the source nonlinearities, which involve both the solution and its gradient. Finally, we present a pseudo-spectral method for computing blow-up solutions to validate our theoretical results.
{"title":"Nonexistence of nontrivial global weak solutions for damping p-Laplacian wave equations with combined nonlinearities","authors":"Yinting Liu , Housen Wang , Qiang Liu","doi":"10.1016/j.cnsns.2026.109801","DOIUrl":"10.1016/j.cnsns.2026.109801","url":null,"abstract":"<div><div>This paper is concerned with the nonexistence of nontrivial global weak solutions for a class of strongly damped wave equations, involving the <em>p</em>-Laplacian term and combined nonlinearities. Employing the test function method, we establish rigorous conditions on the initial data and some exponents that ensure that solutions cannot exist globally in time. In addition, we give an upper bound of lifespan time of the solution. Our results reveal how the strong damping term influences the competition between the <em>p</em>-Laplace operator and the source nonlinearities, which involve both the solution and its gradient. Finally, we present a pseudo-spectral method for computing blow-up solutions to validate our theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109801"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071689","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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