Pub Date : 2026-12-01Epub Date: 2026-02-04DOI: 10.1016/j.nonrwa.2026.104617
Yijie Zha , Xun Cao
This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if , the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if , the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.
{"title":"Threshold dynamics of a reaction-diffusion-advection schistosomiasis model with seasonality","authors":"Yijie Zha , Xun Cao","doi":"10.1016/j.nonrwa.2026.104617","DOIUrl":"10.1016/j.nonrwa.2026.104617","url":null,"abstract":"<div><div>This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span>, the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104617"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116723","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 : 2026-12-01Epub Date: 2026-02-04DOI: 10.1016/j.nonrwa.2026.104615
Xiuwen Li , Zhenhai Liu , Jing Zhao
Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (m-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.
{"title":"Well-posedness results and global attractors for a generalized coupled dynamical system","authors":"Xiuwen Li , Zhenhai Liu , Jing Zhao","doi":"10.1016/j.nonrwa.2026.104615","DOIUrl":"10.1016/j.nonrwa.2026.104615","url":null,"abstract":"<div><div>Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (<em>m</em>-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104615"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116724","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 : 2026-10-01Epub Date: 2026-01-07DOI: 10.1016/j.nonrwa.2025.104600
Andaluzia Matei
In the present paper we draw attention to a strongly coupled nonlinear system consisting of two variational inequalities. Such a system can arise from weak formulations of contact models with implicit material laws governed by non additively-separable g-bipotentials. A multi-contact model applying to an implicit standard material illustrates the theory. Firstly, we deliver abstract results. Then, we apply the abstract results to the well-posedness of the multi-contact model under consideration.
{"title":"Nonlinear variational systems related to contact models with implicit material laws","authors":"Andaluzia Matei","doi":"10.1016/j.nonrwa.2025.104600","DOIUrl":"10.1016/j.nonrwa.2025.104600","url":null,"abstract":"<div><div>In the present paper we draw attention to a strongly coupled nonlinear system consisting of two variational inequalities. Such a system can arise from weak formulations of contact models with implicit material laws governed by non additively-separable g-bipotentials. A multi-contact model applying to an implicit standard material illustrates the theory. Firstly, we deliver abstract results. Then, we apply the abstract results to the well-posedness of the multi-contact model under consideration.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104600"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926981","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 : 2026-10-01Epub Date: 2025-12-18DOI: 10.1016/j.nonrwa.2025.104562
Lin Zhao, Yini Liu
In this paper, we focus on a Zika virus model with diffusion and constant recruitment and analyze the existence and non-existence of traveling wave solutions of the model, which are determined by the basic reproduction number R0 and the minimal wave speed c*. Precisely speaking, if R0 > 1, then there exists a minimal wave speed c* > 0 such that the model admits traveling wave solutions with the wave speed c ≥ c*, and there are no non-trivial traveling wave solutions of this model with 0 < c < c*. If R0 ≤ 1, we prove that there are no non-trivial traveling wave solutions of the model. Finally, numerical simulations are carried out to verify and demonstrate some of the conclusions obtained in this study.
本文研究了一种具有扩散和不断招募的Zika病毒模型，分析了该模型的行波解的存在性和不存在性，其存在性由基本繁殖数R0和最小波速c*决定。准确地讲,如果R0 祝辞 1,那么存在一个最小波速c * 祝辞 0这样的模型承认行波解和波速c ≥ c *,并且没有不平凡的这个模型的行波解与0 & lt; c & lt; c *。当R0 ≤ 1时，我们证明了模型不存在非平凡行波解。最后，通过数值模拟验证和论证了本文的部分结论。
{"title":"Propagation dynamics of a Zika virus model with diffusion and constant recruitment","authors":"Lin Zhao, Yini Liu","doi":"10.1016/j.nonrwa.2025.104562","DOIUrl":"10.1016/j.nonrwa.2025.104562","url":null,"abstract":"<div><div>In this paper, we focus on a Zika virus model with diffusion and constant recruitment and analyze the existence and non-existence of traveling wave solutions of the model, which are determined by the basic reproduction number <em>R</em><sub>0</sub> and the minimal wave speed <em>c</em>*. Precisely speaking, if <em>R</em><sub>0</sub> > 1, then there exists a minimal wave speed <em>c</em>* > 0 such that the model admits traveling wave solutions with the wave speed <em>c</em> ≥ <em>c</em>*, and there are no non-trivial traveling wave solutions of this model with 0 < <em>c</em> < <em>c</em>*. If <em>R</em><sub>0</sub> ≤ 1, we prove that there are no non-trivial traveling wave solutions of the model. Finally, numerical simulations are carried out to verify and demonstrate some of the conclusions obtained in this study.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104562"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791715","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 : 2026-10-01Epub 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":"2026-10-01","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 : 2026-10-01Epub Date: 2026-02-04DOI: 10.1016/j.nonrwa.2026.104616
A. Prabal, M. Devakar
In this paper, we present an analysis that establishes the existence and uniqueness of weak solution of the nonlinear system of partial differential equations governing the steady flow of an incompressible micropolar fluid flow through a homogeneous porous medium in a curved pipe. The Galerkin method along with a version of the Leray-Schauder principle has been used to prove the existence of a weak solution. It has been proved that there is a weak solution for sufficiently small values of curvature ratio (δ); furthermore, it has also been established that the solution is unique for sufficiently small values of Reynolds number (Re) and the micropolarity parameter (m). The regularity of the weak solution is also discussed in this paper; more importantly, if the cross-sectional area (Ω) is sufficiently smooth, specifically of class C3, then the weak solution becomes a classical solution.
{"title":"On the existence, uniqueness and regularity of solutions of micropolar fluid flow through porous medium in a curved pipe","authors":"A. Prabal, M. Devakar","doi":"10.1016/j.nonrwa.2026.104616","DOIUrl":"10.1016/j.nonrwa.2026.104616","url":null,"abstract":"<div><div>In this paper, we present an analysis that establishes the existence and uniqueness of weak solution of the nonlinear system of partial differential equations governing the steady flow of an incompressible micropolar fluid flow through a homogeneous porous medium in a curved pipe. The Galerkin method along with a version of the Leray-Schauder principle has been used to prove the existence of a weak solution. It has been proved that there is a weak solution for sufficiently small values of curvature ratio (<em>δ</em>); furthermore, it has also been established that the solution is unique for sufficiently small values of Reynolds number (<em>Re</em>) and the micropolarity parameter (<em>m</em>). The regularity of the weak solution is also discussed in this paper; more importantly, if the cross-sectional area (Ω) is sufficiently smooth, specifically of class <em>C</em><sup>3</sup>, then the weak solution becomes a classical solution.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104616"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188913","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 : 2026-10-01Epub Date: 2025-12-24DOI: 10.1016/j.nonrwa.2025.104560
Liyan Pang , Xiao Zhang
In this paper, the long time behavior for a two-species Lotka-Volterra reaction-diffusion system with strong competition in a periodic medium is concerned. We prove that under the compactly supported initial values, the solutions of Cauchy problem converge to a pair of diverging pulsating fronts. Further, we obtain a sufficient condition for solutions to converge to 1 with two different speeds to the left and right. Due to the spatial heterogeneity, the pulsating fronts depend on its direction and any pair of rightward and leftward wave speeds be asymmetrical. Therefore, our analysis mainly depends on constructing appropriate super- and subsolutions and using the comparison principle and asymptotic behavior of bistable pulsating fronts.
{"title":"Long time behavior for a Lotka-Volterra competition diffusion system in periodic medium","authors":"Liyan Pang , Xiao Zhang","doi":"10.1016/j.nonrwa.2025.104560","DOIUrl":"10.1016/j.nonrwa.2025.104560","url":null,"abstract":"<div><div>In this paper, the long time behavior for a two-species Lotka-Volterra reaction-diffusion system with strong competition in a periodic medium is concerned. We prove that under the compactly supported initial values, the solutions of Cauchy problem converge to a pair of diverging pulsating fronts. Further, we obtain a sufficient condition for solutions to converge to <strong><em>1</em></strong> with two different speeds to the left and right. Due to the spatial heterogeneity, the pulsating fronts depend on its direction and any pair of rightward and leftward wave speeds be asymmetrical. Therefore, our analysis mainly depends on constructing appropriate super- and subsolutions and using the comparison principle and asymptotic behavior of bistable pulsating fronts.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104560"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841573","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 : 2026-10-01Epub Date: 2025-12-22DOI: 10.1016/j.nonrwa.2025.104585
Fábio Natali
In this paper, we consider the problem of well-posedness and orbital stability of odd periodic traveling waves for the sine-Gordon equation. We first establish novel results concerning the local well-posedness in smoother periodic Sobolev spaces to guarantee the existence of a local time where the associated Cauchy problem has a unique solution with the zero mean property. Afterwards, we prove the orbital stability of odd periodic waves using a convenient index theorem applied to the constrained linearized operator defined in the Sobolev space with the zero mean property.
{"title":"Remarks on the orbital stability for the sine-Gordon equation","authors":"Fábio Natali","doi":"10.1016/j.nonrwa.2025.104585","DOIUrl":"10.1016/j.nonrwa.2025.104585","url":null,"abstract":"<div><div>In this paper, we consider the problem of well-posedness and orbital stability of odd periodic traveling waves for the sine-Gordon equation. We first establish novel results concerning the local well-posedness in smoother periodic Sobolev spaces to guarantee the existence of a local time where the associated Cauchy problem has a unique solution with the zero mean property. Afterwards, we prove the orbital stability of odd periodic waves using a convenient index theorem applied to the constrained linearized operator defined in the Sobolev space with the zero mean property.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104585"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841568","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 : 2026-10-01Epub 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":"2026-10-01","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 : 2026-10-01Epub 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":"2026-10-01","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}
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