Pub Date : 2025-12-16DOI: 10.1016/j.nonrwa.2025.104571
Giuseppe Cardone , Reine Gladys Noucheun , Carmen Perugia , Jean Louis Woukeng
We derive, through the periodic homogenization theory in thin heterogeneous domains, a 2D model consisting of Hele-Shaw equation coupled with the convective Cahn-Hilliard equation with non-constant mobility. The upscaled set of equations, which models in particular tumor growth, is then analyzed and we prove some regularity results. We heavily rely on the two-scale convergence concept in thin heterogeneous media associated to some Sobolev inequalities such as the Gagliardo-Nirenberg and Agmon inequalities to achieve our goal.
{"title":"Mathematical derivation and analysis of a mixture model of tumor growth","authors":"Giuseppe Cardone , Reine Gladys Noucheun , Carmen Perugia , Jean Louis Woukeng","doi":"10.1016/j.nonrwa.2025.104571","DOIUrl":"10.1016/j.nonrwa.2025.104571","url":null,"abstract":"<div><div>We derive, through the periodic homogenization theory in thin heterogeneous domains, a 2<em>D</em> model consisting of Hele-Shaw equation coupled with the convective Cahn-Hilliard equation with non-constant mobility. The upscaled set of equations, which models in particular tumor growth, is then analyzed and we prove some regularity results. We heavily rely on the two-scale convergence concept in thin heterogeneous media associated to some Sobolev inequalities such as the Gagliardo-Nirenberg and Agmon inequalities to achieve our goal.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104571"},"PeriodicalIF":1.8,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791713","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}
Pub Date : 2025-12-15DOI: 10.1016/j.nonrwa.2025.104561
Xinshan Dong , Ben Niu , Lin Wang
We investigate a diffusive Rosenzweig-MacArthur system that includes nonlocal prey competition and prey-taxis under Neumann boundary conditions. Initially, we establish the global existence and boundedness of solutions for arbitrary spatial dimensions and small prey-taxis sensitivity coefficient. Subsequently, we analyze the local stability of the constant steady-state solution. Using the Lyapunov-Schmidt reduction method, we explore several bifurcations near the positive constant steady-state: steady-state bifurcation, Hopf bifurcation, and their interaction. Finally, numerical simulations are performed to validate our theoretical findings and illustrate complex spatiotemporal patterns. By selecting appropriate parameters and initial conditions, our simulations reveal the coexistence of a pair of stable spatially nonhomogeneous steady-states and stable spatially homogeneous periodic solutions, which indicates the system exhibits tristability, that is, the coexistence of three distinct stable states. Moreover, our results demonstrate that transient patterns transition from spatially nonhomogeneous periodic solutions to spatially nonhomogeneous steady-state and spatially homogeneous periodic solutions.
{"title":"Spatiotemporal patterns induced by nonlocal prey competition and prey-taxis in a diffusive Rosenzweig-MacArthur system","authors":"Xinshan Dong , Ben Niu , Lin Wang","doi":"10.1016/j.nonrwa.2025.104561","DOIUrl":"10.1016/j.nonrwa.2025.104561","url":null,"abstract":"<div><div>We investigate a diffusive Rosenzweig-MacArthur system that includes nonlocal prey competition and prey-taxis under Neumann boundary conditions. Initially, we establish the global existence and boundedness of solutions for arbitrary spatial dimensions and small prey-taxis sensitivity coefficient. Subsequently, we analyze the local stability of the constant steady-state solution. Using the Lyapunov-Schmidt reduction method, we explore several bifurcations near the positive constant steady-state: steady-state bifurcation, Hopf bifurcation, and their interaction. Finally, numerical simulations are performed to validate our theoretical findings and illustrate complex spatiotemporal patterns. By selecting appropriate parameters and initial conditions, our simulations reveal the coexistence of a pair of stable spatially nonhomogeneous steady-states and stable spatially homogeneous periodic solutions, which indicates the system exhibits tristability, that is, the coexistence of three distinct stable states. Moreover, our results demonstrate that transient patterns transition from spatially nonhomogeneous periodic solutions to spatially nonhomogeneous steady-state and spatially homogeneous periodic solutions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104561"},"PeriodicalIF":1.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791662","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}
Pub Date : 2025-12-15DOI: 10.1016/j.nonrwa.2025.104569
Nguyen Van Y , Le Cong Nhan , Le Xuan Truong
In the paper, we consider a fractional thermo-viscoelastic system with nonlinear sources and study some of its qualitative properties based on the interaction of the fractional viscoelastic and thermal damping with the external forces. By using the theory of linear Volterra differential-integral equations of convolution type and the Banach fixed point theorem, we first prove the local well-posedness and maximal regularity of the weak solution. Then by using the variational and potential well methods, we give a sufficient condition for the continuity in time of the local weak solution when it starts in the potential wells. Besides that the asymptotic behavior of global solution is also concerned, unlike the classical thermoelasticity where the total energy does not decays uniformly, since the effect of the fractional viscoelastic damping, we show that the total energy shall decay uniformly. In addition, its decay rate is given explicitly and optimally in the sense of Lasiecka et. al.[1]. Finally, since the presence of the nonlinear sources, we show that the blow-up phenomenon may occur in finite time provided that the solution starts outside the potential wells and the relaxation function is small in some sense. Also notice that the effect of the thermal damping is not enough to make the total energy decays to zero, but it could retards the blow-up phenomenon.
{"title":"Some qualitative properties of solution to a fractional thermo-viscoelastic system with nonlinear sources","authors":"Nguyen Van Y , Le Cong Nhan , Le Xuan Truong","doi":"10.1016/j.nonrwa.2025.104569","DOIUrl":"10.1016/j.nonrwa.2025.104569","url":null,"abstract":"<div><div>In the paper, we consider a fractional thermo-viscoelastic system with nonlinear sources and study some of its qualitative properties based on the interaction of the fractional viscoelastic and thermal damping with the external forces. By using the theory of linear Volterra differential-integral equations of convolution type and the Banach fixed point theorem, we first prove the local well-posedness and maximal regularity of the weak solution. Then by using the variational and potential well methods, we give a sufficient condition for the continuity in time of the local weak solution when it starts in the potential wells. Besides that the asymptotic behavior of global solution is also concerned, unlike the classical thermoelasticity where the total energy does not decays uniformly, since the effect of the fractional viscoelastic damping, we show that the total energy shall decay uniformly. In addition, its decay rate is given explicitly and optimally in the sense of Lasiecka et. al.[1]. Finally, since the presence of the nonlinear sources, we show that the blow-up phenomenon may occur in finite time provided that the solution starts outside the potential wells and the relaxation function is small in some sense. Also notice that the effect of the thermal damping is not enough to make the total energy decays to zero, but it could retards the blow-up phenomenon.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104569"},"PeriodicalIF":1.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791711","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}
Pub Date : 2025-12-15DOI: 10.1016/j.nonrwa.2025.104577
Manjun Ma, Kaili Wang, Dan Li
This work is concerned with a nonlinear and non-monotonic reaction-diffusion system that models the dynamics of bacterial colonies with density-suppressed motility. We first establish the existence of global solutions and the attractivity of the uniform coexsitence state in a moving coordinate frame. Traveling waves are then transformed into fixed points of a mapping associated with an auxiliary system. By constructing upper and lower solutions, we next establish an invariant function space for this mapping. By using Schauder’s fixed point theorem, we derive implicit conditions for the existence of traveling waves. Through developing innovative analytical techniques, we further obtain explicit conditions that are corroborated by numerical computation and simulations of the considered bacterial colony model.
{"title":"Traveling waves in a bacterial colony model","authors":"Manjun Ma, Kaili Wang, Dan Li","doi":"10.1016/j.nonrwa.2025.104577","DOIUrl":"10.1016/j.nonrwa.2025.104577","url":null,"abstract":"<div><div>This work is concerned with a nonlinear and non-monotonic reaction-diffusion system that models the dynamics of bacterial colonies with density-suppressed motility. We first establish the existence of global solutions and the attractivity of the uniform coexsitence state in a moving coordinate frame. Traveling waves are then transformed into fixed points of a mapping associated with an auxiliary system. By constructing upper and lower solutions, we next establish an invariant function space for this mapping. By using Schauder’s fixed point theorem, we derive implicit conditions for the existence of traveling waves. Through developing innovative analytical techniques, we further obtain explicit conditions that are corroborated by numerical computation and simulations of the considered bacterial colony model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104577"},"PeriodicalIF":1.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791712","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}
Pub Date : 2025-12-13DOI: 10.1016/j.nonrwa.2025.104574
Weidong Qin, Yunxian Dai, Doudou Lou
This paper investigates a delayed predator-prey model incorporating fear effects, prey refuge, Crowley-Martin type functional response, and cross-diffusion. First, we analyze the existence and stability of the positive equilibrium of the non-delay model. Then, we investigate the conditions for the occurrence of Turing instability in the delayed model. The amplitude equation is derived using the multiple-scale perturbation method, revealing the relationship between pattern selection and system parameters. Meanwhile, some numerical simulations are conducted to validate the accuracy of the theoretical analysis. The results demonstrate that varying control parameters can induce diverse patterns, including spots, stripes, and mixed patterns. Additionally, we find that the fear response delay affects the stabilization time of patterns, and as the delay increases, the patterns gradually become unstable. This study highlights the impact of the fear response delay on the stability and pattern formation in predator-prey systems, providing theoretical insights into the complexity of population dynamics.
{"title":"Pattern dynamics in a reaction-diffusion predator-prey model with fear response delay","authors":"Weidong Qin, Yunxian Dai, Doudou Lou","doi":"10.1016/j.nonrwa.2025.104574","DOIUrl":"10.1016/j.nonrwa.2025.104574","url":null,"abstract":"<div><div>This paper investigates a delayed predator-prey model incorporating fear effects, prey refuge, Crowley-Martin type functional response, and cross-diffusion. First, we analyze the existence and stability of the positive equilibrium of the non-delay model. Then, we investigate the conditions for the occurrence of Turing instability in the delayed model. The amplitude equation is derived using the multiple-scale perturbation method, revealing the relationship between pattern selection and system parameters. Meanwhile, some numerical simulations are conducted to validate the accuracy of the theoretical analysis. The results demonstrate that varying control parameters can induce diverse patterns, including spots, stripes, and mixed patterns. Additionally, we find that the fear response delay affects the stabilization time of patterns, and as the delay increases, the patterns gradually become unstable. This study highlights the impact of the fear response delay on the stability and pattern formation in predator-prey systems, providing theoretical insights into the complexity of population dynamics.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104574"},"PeriodicalIF":1.8,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791665","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}
Pub Date : 2025-12-12DOI: 10.1016/j.nonrwa.2025.104575
Xinyu Bo, Qi An, Wenjun Liu, Guangying Lv
Considering the increasing level of international environmental pollution, especially the discharge of nuclear effluents into the oceans, we consider in this paper, the dynamics of a predator-prey model in toxic environments. The concentration of toxins is no longer constant, but is influenced by time and location, and it will interact with predator-prey systems, thereby affecting the dynamic behavior of the entire ecosystem. The boundedness and positive definiteness of the model are obtained by using the comparison principle and the maximum principle. Afterwards, the threshold condition of toxicant concentration for the stability of the steady state solutions and the rate of convergence of the solutions are obtained by using the matrix positive definiteness, Schauder’s theorem and LaSalle’s invariance principle. Finally, numerical examples verify our results.
{"title":"A predator-prey model with poison dependent diffusion","authors":"Xinyu Bo, Qi An, Wenjun Liu, Guangying Lv","doi":"10.1016/j.nonrwa.2025.104575","DOIUrl":"10.1016/j.nonrwa.2025.104575","url":null,"abstract":"<div><div>Considering the increasing level of international environmental pollution, especially the discharge of nuclear effluents into the oceans, we consider in this paper, the dynamics of a predator-prey model in toxic environments. The concentration of toxins is no longer constant, but is influenced by time and location, and it will interact with predator-prey systems, thereby affecting the dynamic behavior of the entire ecosystem. The boundedness and positive definiteness of the model are obtained by using the comparison principle and the maximum principle. Afterwards, the threshold condition of toxicant concentration for the stability of the steady state solutions and the rate of convergence of the solutions are obtained by using the matrix positive definiteness, Schauder’s theorem and LaSalle’s invariance principle. Finally, numerical examples verify our results.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104575"},"PeriodicalIF":1.8,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738910","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}
Pub Date : 2025-12-11DOI: 10.1016/j.nonrwa.2025.104566
Zihao Zhang
This paper concerns subsonic Euler flows in a two-dimensional finitely long slightly curved nozzle under the vertical gravity. Concerning the effect of the vertical gravity, we first establish the existence of subsonic shear flows in the flat nozzle. We then investigate the structural stability of these background subsonic flows under small perturbations of suitable boundary conditions on the entrance and exit and the upper and lower nozzle walls. It can be formulated as a nonlinear boundary value problem for a hyperbolic-elliptic mixed system. The main difficulty is that all the physical quantities are coupled with each other due to the existence of the vertical gravity. The approach is based on the Lagrangian transformation to straighten the streamline and the deformation-curl decomposition to deal with the hyperbolic and elliptic modes in the subsonic region. The key ingredient of the analysis is to solve the associated linearized elliptic boundary value problem with mixed boundary conditions in a weighted Hölder space.
{"title":"Subsonic Euler flows with gravity in a two-dimensional finitely long curved nozzle","authors":"Zihao Zhang","doi":"10.1016/j.nonrwa.2025.104566","DOIUrl":"10.1016/j.nonrwa.2025.104566","url":null,"abstract":"<div><div>This paper concerns subsonic Euler flows in a two-dimensional finitely long slightly curved nozzle under the vertical gravity. Concerning the effect of the vertical gravity, we first establish the existence of subsonic shear flows in the flat nozzle. We then investigate the structural stability of these background subsonic flows under small perturbations of suitable boundary conditions on the entrance and exit and the upper and lower nozzle walls. It can be formulated as a nonlinear boundary value problem for a hyperbolic-elliptic mixed system. The main difficulty is that all the physical quantities are coupled with each other due to the existence of the vertical gravity. The approach is based on the Lagrangian transformation to straighten the streamline and the deformation-curl decomposition to deal with the hyperbolic and elliptic modes in the subsonic region. The key ingredient of the analysis is to solve the associated linearized elliptic boundary value problem with mixed boundary conditions in a weighted Hölder space.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104566"},"PeriodicalIF":1.8,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747402","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}
Pub Date : 2025-12-11DOI: 10.1016/j.nonrwa.2025.104564
Aiping Zhang, Zesheng Feng, Hongya Gao
This paper deals with a class of non-uniformly polyconvex integral functionals with splitting form in 3-dimensional Euclidean space. Under some structural conditions on the energy density, we prove that each component uα of local minimizer u is locally bounded. Our approach is based on a suitable adaptation of the celebrated De Giorgi’s iterative method, and it relies on an appropriate Caccioppoli-type inequality. Our result can be applied to the polyconvex integralwith suitable functions λ(x) > 0, b(x) ≥ 0 and exponents p, q > 1, r, s ≥ 1.
研究了三维欧几里德空间中一类具有分裂形式的非一致多凸积分泛函。在能量密度的某些结构条件下，证明了局部极小器u的各分量uα是局部有界的。我们的方法是基于著名的De Giorgi的迭代方法的适当改编，它依赖于一个适当的caccioppolii型不等式。我们的结果可以应用于polyconvex积分∫Ω{∑α= 13(λ(x) | Duα| p + | (adj2Du)α| q] + | detDu | r +∑α= 13 b (x) | uα|年代}dxwith合适功能λ(x) 祝辞 0 b (x) ≥ 0和指数p, q 祝辞 1,r, s ≥ 1。
{"title":"Local boundedness for minimizers of some non-uniformly polyconvex integrals","authors":"Aiping Zhang, Zesheng Feng, Hongya Gao","doi":"10.1016/j.nonrwa.2025.104564","DOIUrl":"10.1016/j.nonrwa.2025.104564","url":null,"abstract":"<div><div>This paper deals with a class of non-uniformly polyconvex integral functionals with splitting form in 3-dimensional Euclidean space. Under some structural conditions on the energy density, we prove that each component <em>u<sup>α</sup></em> of local minimizer <em>u</em> is locally bounded. Our approach is based on a suitable adaptation of the celebrated De Giorgi’s iterative method, and it relies on an appropriate Caccioppoli-type inequality. Our result can be applied to the polyconvex integral<span><span><span><math><mrow><msub><mo>∫</mo><mstyle><mi>Ω</mi></mstyle></msub><mrow><mo>{</mo><munderover><mo>∑</mo><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mrow><mo>[</mo><mi>λ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo><mi>D</mi></mrow><msup><mi>u</mi><mi>α</mi></msup><msup><mrow><mo>|</mo></mrow><mi>p</mi></msup><mrow><mo>+</mo><mo>|</mo></mrow><msup><mrow><mo>(</mo><msub><mrow><mrow><mi>a</mi></mrow><mi>d</mi><mi>j</mi></mrow><mn>2</mn></msub><mi>D</mi><mi>u</mi><mo>)</mo></mrow><mi>α</mi></msup><msup><mrow><mo>|</mo></mrow><mi>q</mi></msup><msup><mrow><mo>]</mo><mo>+</mo><mo>|</mo><mi>det</mi><mi>D</mi><mi>u</mi><mo>|</mo></mrow><mi>r</mi></msup><mo>+</mo><munderover><mo>∑</mo><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mo>|</mo><msup><mi>u</mi><mi>α</mi></msup><mo>|</mo></mrow><mi>s</mi></msup><mo>}</mo></mrow><mrow><mi>d</mi></mrow><mi>x</mi></mrow></math></span></span></span>with suitable functions <em>λ</em>(<em>x</em>) > 0, <em>b</em>(<em>x</em>) ≥ 0 and exponents <em>p, q</em> > 1, <em>r, s</em> ≥ 1.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104564"},"PeriodicalIF":1.8,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747406","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}
Pub Date : 2025-12-10DOI: 10.1016/j.nonrwa.2025.104576
Ken Abe
We consider the stability of magnetohydrostatic (MHS) equilibria in the ideal MHD equations in a bounded and simply connected domain . We show that the set of magnetic energy minimizers with constant helicity (i.e., linear force-free fields) is Lyapunov stable among the weak ideal limits of Leray–Hopf solutions to the viscous and resistive MHD equations.
{"title":"Stability of force-free fields in weak ideal limits of Leray–Hopf solutions I: Linear force-free fields","authors":"Ken Abe","doi":"10.1016/j.nonrwa.2025.104576","DOIUrl":"10.1016/j.nonrwa.2025.104576","url":null,"abstract":"<div><div>We consider the stability of magnetohydrostatic (MHS) equilibria in the ideal MHD equations in a bounded and simply connected domain <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mn>3</mn></msup></mrow></math></span>. We show that the set of magnetic energy minimizers with constant helicity (i.e., linear force-free fields) is Lyapunov stable among the weak ideal limits of Leray–Hopf solutions to the viscous and resistive MHD equations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104576"},"PeriodicalIF":1.8,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747403","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}
Pub Date : 2025-12-10DOI: 10.1016/j.nonrwa.2025.104563
Christian Kuehn , Jaeyoung Yoon
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of the Cucker-Smale and Hegselmann-Krause models to a combined adaptive (or co-evolutionary) network. Reducing our model to a singular limit of fast adaptation, we mathematically analyze the asymptotic behavior of the resulting Laplacian dynamics over various classes of temporal graphs and use these results to explain the behavior of the original proposed adaptive model for fast adaptation. In particular, our approach provides a general methodology for analyzing linear consensus models over time-varying networks that naturally arise as singular limits in many adaptive network models.
{"title":"Adaptive Cucker-Smale networks: Limiting Laplacian time-varying dynamics","authors":"Christian Kuehn , Jaeyoung Yoon","doi":"10.1016/j.nonrwa.2025.104563","DOIUrl":"10.1016/j.nonrwa.2025.104563","url":null,"abstract":"<div><div>Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of the Cucker-Smale and Hegselmann-Krause models to a combined adaptive (or co-evolutionary) network. Reducing our model to a singular limit of fast adaptation, we mathematically analyze the asymptotic behavior of the resulting Laplacian dynamics over various classes of temporal graphs and use these results to explain the behavior of the original proposed adaptive model for fast adaptation. In particular, our approach provides a general methodology for analyzing linear consensus models over time-varying networks that naturally arise as singular limits in many adaptive network models.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104563"},"PeriodicalIF":1.8,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747404","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}
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