Pub Date : 2025-12-24DOI: 10.1016/j.nonrwa.2025.104581
L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon
In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree n, separated by the straight line . Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy , the system admits at most limit cycles. Furthermore, for the specific case , assuming d2 ≠ M2 and , we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.
{"title":"Limit cycles on rigid piecewise smooth dynamical systems governed by even polynomials","authors":"L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon","doi":"10.1016/j.nonrwa.2025.104581","DOIUrl":"10.1016/j.nonrwa.2025.104581","url":null,"abstract":"<div><div>In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree <em>n</em>, separated by the straight line <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><msub><mi>M</mi><mn>2</mn></msub></mrow></math></span>, the system admits at most <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>2</mn></mrow></math></span> limit cycles. Furthermore, for the specific case <span><math><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></math></span>, assuming <em>d</em><sub>2</sub> ≠ <em>M</em><sub>2</sub> and <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span>, we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104581"},"PeriodicalIF":1.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841571","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 : 2025-12-24DOI: 10.1016/j.nonrwa.2025.104584
Ifeanyi Sunday Onah
This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number Rv and establish conditions for the stability of the disease-free periodic solution. When Rv < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for Rv > 1, the infection is uniformly persistent and the system admits at least one positive T-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce Rv below one and interrupt sustained transmission.
{"title":"Seasonal dynamics and control of malaria: A non-autonomous model incorporating vaccination and drug resistance","authors":"Ifeanyi Sunday Onah","doi":"10.1016/j.nonrwa.2025.104584","DOIUrl":"10.1016/j.nonrwa.2025.104584","url":null,"abstract":"<div><div>This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number <em>R<sub>v</sub></em> and establish conditions for the stability of the disease-free periodic solution. When <em>R<sub>v</sub></em> < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for <em>R<sub>v</sub></em> > 1, the infection is uniformly persistent and the system admits at least one positive <em>T</em>-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce <em>R<sub>v</sub></em> below one and interrupt sustained transmission.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104584"},"PeriodicalIF":1.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841572","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 : 2025-12-24DOI: 10.1016/j.nonrwa.2025.104580
Leander Claes , Michael Winkler
<div><div>In bounded <em>n</em>-dimensional domains with <em>n</em> ≥ 1, this manuscript examines an initial-boundary value problem for the system<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mi>f</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mstyle><mi>Θ</mi></mstyle><mi>t</mi></msub><mo>=</mo><mi>D</mi><mstyle><mi>Δ</mi></mstyle><mstyle><mi>Θ</mi></mstyle><mo>+</mo><mstyle><mi>Γ</mi></mstyle><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><msup><mrow><mo>|</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>|</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>·</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>which in the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and with <em>γ</em> ≡ Γ as well as <em>f</em> ≡ <em>F</em> reduces to the classical model for the evolution of displacement and temperatures in thermoviscoelasticity. Unlike in previous related studies, the focus here is on situations in which besides <em>f</em> and <em>F</em>, also the core ingredients <em>γ</em> and Γ may depend on the temperature variable Θ. Firstly, a statement on local existence of classical solutions is derived for arbitrary <em>a</em> > 0, <em>D</em> > 0 as well as 0 < <em>γ</em> ∈ <em>C</em><sup>2</sup>([0, ∞)) and 0 ≤ Γ ∈ <em>C</em><sup>1</sup>([0, ∞)), for functions <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>F</mi><mo>∈</mo><msup><mi>C</mi><mn>1</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math></span>, and for suitably regular initial data of arbitrary size. Secondly, it is seen that under an additional assumption on smallness of <em>a, f</em>′ and <em>F</em>, as well as on the deviation of the initial data from the constant state given by <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mstyle><mi>Θ</mi></mstyle><mo>=</mo><msub><mstyle><mi>Θ</mi></mstyle><mi>★</mi>
{"title":"Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic system by W1,p energy analysis","authors":"Leander Claes , Michael Winkler","doi":"10.1016/j.nonrwa.2025.104580","DOIUrl":"10.1016/j.nonrwa.2025.104580","url":null,"abstract":"<div><div>In bounded <em>n</em>-dimensional domains with <em>n</em> ≥ 1, this manuscript examines an initial-boundary value problem for the system<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mi>f</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mstyle><mi>Θ</mi></mstyle><mi>t</mi></msub><mo>=</mo><mi>D</mi><mstyle><mi>Δ</mi></mstyle><mstyle><mi>Θ</mi></mstyle><mo>+</mo><mstyle><mi>Γ</mi></mstyle><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><msup><mrow><mo>|</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>|</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>·</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>which in the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and with <em>γ</em> ≡ Γ as well as <em>f</em> ≡ <em>F</em> reduces to the classical model for the evolution of displacement and temperatures in thermoviscoelasticity. Unlike in previous related studies, the focus here is on situations in which besides <em>f</em> and <em>F</em>, also the core ingredients <em>γ</em> and Γ may depend on the temperature variable Θ. Firstly, a statement on local existence of classical solutions is derived for arbitrary <em>a</em> > 0, <em>D</em> > 0 as well as 0 < <em>γ</em> ∈ <em>C</em><sup>2</sup>([0, ∞)) and 0 ≤ Γ ∈ <em>C</em><sup>1</sup>([0, ∞)), for functions <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>F</mi><mo>∈</mo><msup><mi>C</mi><mn>1</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math></span>, and for suitably regular initial data of arbitrary size. Secondly, it is seen that under an additional assumption on smallness of <em>a, f</em>′ and <em>F</em>, as well as on the deviation of the initial data from the constant state given by <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mstyle><mi>Θ</mi></mstyle><mo>=</mo><msub><mstyle><mi>Θ</mi></mstyle><mi>★</mi>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104580"},"PeriodicalIF":1.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841569","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 : 2025-12-23DOI: 10.1016/j.nonrwa.2025.104573
Rafael Muñoz-Sola
The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.
{"title":"Mathematical analysis of a levitation model","authors":"Rafael Muñoz-Sola","doi":"10.1016/j.nonrwa.2025.104573","DOIUrl":"10.1016/j.nonrwa.2025.104573","url":null,"abstract":"<div><div>The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104573"},"PeriodicalIF":1.8,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841567","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 : 2025-12-22DOI: 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":"2025-12-22","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 : 2025-12-22DOI: 10.1016/j.nonrwa.2025.104583
Qian Jiang , Zhijun Liu , Lianwen Wang
This work proposes a novel age-structured tuberculosis (TB) model to evaluate the impact of pre- and post-exposure vaccinations on TB control, explicitly incorporating the waning of vaccine-induced efficacy over time. Mathematically, we establish a broadly applicable analytical framework for rigorously proving the global stability of steady states in the age-structured model. Furthermore, we formulate an optimal control problem with time-dependent vaccination schedules, identifying cost-effective vaccination strategies under realistic resource constraints. Epidemiologically, our analysis indicates that a combined vaccination strategy is most effective overall. While pre-exposure vaccination proves superior for long-term outbreak control, high-intensity post-exposure vaccination is crucial in high-exposure scenarios to rapidly reduce infected cases. This offers valuable insights for evaluating vaccination-based prevention and control strategies.
{"title":"Global stability analysis and optimal vaccination strategy for an age-structured tuberculosis model with general incidence","authors":"Qian Jiang , Zhijun Liu , Lianwen Wang","doi":"10.1016/j.nonrwa.2025.104583","DOIUrl":"10.1016/j.nonrwa.2025.104583","url":null,"abstract":"<div><div>This work proposes a novel age-structured tuberculosis (TB) model to evaluate the impact of pre- and post-exposure vaccinations on TB control, explicitly incorporating the waning of vaccine-induced efficacy over time. Mathematically, we establish a broadly applicable analytical framework for rigorously proving the global stability of steady states in the age-structured model. Furthermore, we formulate an optimal control problem with time-dependent vaccination schedules, identifying cost-effective vaccination strategies under realistic resource constraints. Epidemiologically, our analysis indicates that a combined vaccination strategy is most effective overall. While pre-exposure vaccination proves superior for long-term outbreak control, high-intensity post-exposure vaccination is crucial in high-exposure scenarios to rapidly reduce infected cases. This offers valuable insights for evaluating vaccination-based prevention and control strategies.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104583"},"PeriodicalIF":1.8,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841566","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 : 2025-12-19DOI: 10.1016/j.nonrwa.2025.104578
Jilei Huang, Peidong Lei, Junquan Zhou
In this paper, we prove controllability results for non-dissipative heat equations under natural unilateral constraints on the control. When the controlled parabolic system is non-dissipative, the controllability under nonnegative control constraints may fail in large time for general L2-initial data and final target trajectories. We establish the controllability of the general target trajectory when the difference between the initial states of the controlled system and the target trajectory lies within a specified subspace of L2(Ω). Conversely, if the difference lies outside this subspace, we prove that there exist infinitely many initial states causing system uncontrollability. We also prove that under nonnegative control constraints, there exists a minimum positive time required to achieve general target trajectory controllability, showing a waiting time phenomenon.
{"title":"Controllability of non-dissipative heat equations under unilateral control constraints","authors":"Jilei Huang, Peidong Lei, Junquan Zhou","doi":"10.1016/j.nonrwa.2025.104578","DOIUrl":"10.1016/j.nonrwa.2025.104578","url":null,"abstract":"<div><div>In this paper, we prove controllability results for non-dissipative heat equations under natural unilateral constraints on the control. When the controlled parabolic system is non-dissipative, the controllability under nonnegative control constraints may fail in large time for general <em>L</em><sup>2</sup>-initial data and final target trajectories. We establish the controllability of the general target trajectory when the difference between the initial states of the controlled system and the target trajectory lies within a specified subspace of <em>L</em><sup>2</sup>(Ω). Conversely, if the difference lies outside this subspace, we prove that there exist infinitely many initial states causing system uncontrollability. We also prove that under nonnegative control constraints, there exists a minimum positive time required to achieve general target trajectory controllability, showing a waiting time phenomenon.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104578"},"PeriodicalIF":1.8,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791714","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 : 2025-12-19DOI: 10.1016/j.nonrwa.2025.104521
Luiz Fernando Gonçalves, Bruno Rodrigues Freitas, Ronaldo Alves Garcia
In this paper, we investigate the existence of limit cycles in a class of planar piecewise smooth differential systems having the unit circle as their switching manifold. The vector field inside the circle is assumed to be linear and Hamiltonian, while the vector field outside is given by . We provide an upper bound for the number of crossing limit cycles such systems can possess, as well as for some of their perturbations.
{"title":"Limit cycles in a class of piecewise polynomial differential systems having the unit circle as their switching manifold","authors":"Luiz Fernando Gonçalves, Bruno Rodrigues Freitas, Ronaldo Alves Garcia","doi":"10.1016/j.nonrwa.2025.104521","DOIUrl":"10.1016/j.nonrwa.2025.104521","url":null,"abstract":"<div><div>In this paper, we investigate the existence of limit cycles in a class of planar piecewise smooth differential systems having the unit circle as their switching manifold. The vector field inside the circle is assumed to be linear and Hamiltonian, while the vector field outside is given by <span><math><mrow><mover><mi>z</mi><mo>˙</mo></mover><mo>=</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></math></span>. We provide an upper bound for the number of crossing limit cycles such systems can possess, as well as for some of their perturbations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104521"},"PeriodicalIF":1.8,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791743","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 : 2025-12-18DOI: 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。
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Pub Date : 2025-12-18DOI: 10.1016/j.nonrwa.2025.104570
Paolo Piersanti
In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is of Signorini type, and is given over the boundary of the linearly viscoelastic body under consideration. We show that one such variational problem admits solutions and we coin a novel concept of solution which, differently from the available literature, is valid even in the case where the viscoelastic body starts its motion in contact with the obstacle. Additionally, under additional assumptions on the constituting material, we show that when the applied body force is lifted the deformed linearly viscoelastic body returns to its rest position at an exponential rate of decay.
{"title":"Existence of solutions for time-dependent Signorini-type problems in linearised viscoelasticity","authors":"Paolo Piersanti","doi":"10.1016/j.nonrwa.2025.104570","DOIUrl":"10.1016/j.nonrwa.2025.104570","url":null,"abstract":"<div><div>In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is of Signorini type, and is given over the boundary of the linearly viscoelastic body under consideration. We show that one such variational problem admits solutions and we coin a novel concept of solution which, differently from the available literature, is valid even in the case where the viscoelastic body starts its motion in contact with the obstacle. Additionally, under additional assumptions on the constituting material, we show that when the applied body force is lifted the deformed linearly viscoelastic body returns to its rest position at an exponential rate of decay.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104570"},"PeriodicalIF":1.8,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791716","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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