Pub 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":"2026-02-04","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 : 2026-02-04DOI: 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":"2026-02-04","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 : 2026-01-30DOI: 10.1016/j.nonrwa.2026.104611
Rongrong Yan , Bin Guo , Xiangyu Zhu
In this paper, we consider an initial boundary value problem for the following Timoshenko equation with variable exponents:
First of all, we combine the truncation method, energy estimate method and Banach fixed point theorem as well as Galerkin method to prove the existence of local solutions with the exponent q(x) satisfying Subsequently, for the supercritical case(), owing to the failure of the embedding inequality, the well-known multiplier technique is unsuccessful in our problem. To end this, our strategy is to give a priori estimate for the weighted integral , and then to apply modified weighted multiplier method and potential well method to prove that the energy functional decays logarithmically under this condition. In particular, these results reveal the explicit relationship between decay rate of solutions and the weak damping term. These results improved and extended the existing results [1, 2].
本文考虑了下述变指数Timoshenko方程的初边值问题：utt+Δ2u−M（∥∇u∥2）Δu+| but | M(x)−2ut=|u|q(x)−2u。首先，结合截断法、能量估计法和Banach不动点定理以及Galerkin方法，证明了指数q(x)满足2(n−2)n−4<q(x)<；2nn−4的局部解的存在性。随后，对于超临界情况（m(x)>2nn−4），由于嵌入不等式的失效，众所周知的乘子技术在我们的问题中是不成功的。为此，我们的策略是对加权积分∫Ω（2+t）1−m(x)|u|m(x)dx进行先验估计，然后应用改进的加权乘数法和势阱法证明能量泛函在这种情况下呈对数衰减。特别地，这些结果揭示了解的衰减率与弱阻尼项之间的显式关系。这些结果是对已有结果的改进和扩展[1,2]。
{"title":"Existence and decay of solutions for Timoshenko-type equation with variable exponents and the supercritical damping","authors":"Rongrong Yan , Bin Guo , Xiangyu Zhu","doi":"10.1016/j.nonrwa.2026.104611","DOIUrl":"10.1016/j.nonrwa.2026.104611","url":null,"abstract":"<div><div>In this paper, we consider an initial boundary value problem for the following Timoshenko equation with variable exponents:<span><span><span><math><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><msup><mstyle><mi>Δ</mi></mstyle><mn>2</mn></msup><mspace></mspace><mi>u</mi><mo>−</mo><msup><mrow><mi>M</mi><mo>(</mo><mo>∥</mo><mi>∇</mi><mi>u</mi><mo>∥</mo></mrow><mn>2</mn></msup><mrow><mo>)</mo><mstyle><mi>Δ</mi></mstyle><mi>u</mi><mo>+</mo><mo>|</mo></mrow><msub><mi>u</mi><mi>t</mi></msub><msup><mrow><mo>|</mo></mrow><mrow><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>.</mo></mrow></math></span></span></span></div><div>First of all, we combine the truncation method, energy estimate method and Banach fixed point theorem as well as Galerkin method to prove the existence of local solutions with the exponent <em>q</em>(<em>x</em>) satisfying <span><math><mrow><mfrac><mrow><mn>2</mn><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>n</mi><mo>−</mo><mn>4</mn></mrow></mfrac><mo><</mo><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo><</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>4</mn></mrow></mfrac><mo>.</mo></mrow></math></span> Subsequently, for the supercritical case(<span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>></mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>4</mn></mrow></mfrac></mrow></math></span>), owing to the failure of the embedding inequality, the well-known multiplier technique is unsuccessful in our problem. To end this, our strategy is to give a priori estimate for the weighted integral <span><math><mstyle><mrow><msub><mo>∫</mo><mstyle><mi>Ω</mi></mstyle></msub><msup><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>−</mo><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mrow><mi>d</mi></mrow><mi>x</mi></mrow></mstyle></math></span>, and then to apply modified weighted multiplier method and potential well method to prove that the energy functional decays logarithmically under this condition. In particular, these results reveal the explicit relationship between decay rate of solutions and the weak damping term. These results improved and extended the existing results [1, 2].</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104611"},"PeriodicalIF":1.8,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077474","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 : 2026-01-29DOI: 10.1016/j.nonrwa.2026.104610
Petar Ćirković , Jelena V. Manojlović
The present paper discusses the dynamics and optimal harvesting of an intraguild predation three-level food web model incorporating nonlinear Michaelis-Menten type harvesting on the intermediate predator and proportional harvesting on the intraguild predator. The positivity and boundedness of solutions, as well as the existence and stability of equilibria, are established, and unconditional survival of the prey species is observed. The effect of harvesting is studied through a detailed bifurcation analysis, revealing rich dynamical behaviors and threshold harvesting levels that prevent predator extinction. The existence of saddle-node, transcritical, pitchfork, and Hopf bifurcations is shown. The qualitative dynamics are discussed through two-parameter bifurcation diagram. Parameter regions of extinction and coexistence are identified. At higher harvesting rates, Bogdanov-Takens and generalized Hopf bifurcations reveal parametric regions in which either both predator species will eventually be driven to extinction or all three species may coexist, depending on the initial values. At lower harvesting rates, Zero-Hopf and generalized Hopf bifurcations reveal parametric regions in which either intermediate predator eventually goes extinct or all three species may coexist, depending on the initial population densities. It is shown that the system can exhibit multistability and sensitivity to initial conditions, with bistability between coexistence attractors and predator-free attractors. From an economic perspective, an optimal harvesting policy is derived, maximizing the total economic return from harvesting while preventing overharvesting and ensuring ecological sustainability. A numerical example shows that both economic benefits and ecological balance can be achieved by controlling both predators harvesting rates.
{"title":"Bifurcation analysis and optimal harvesting of an intraguild predation three-level food web model with harvesting on top two levels","authors":"Petar Ćirković , Jelena V. Manojlović","doi":"10.1016/j.nonrwa.2026.104610","DOIUrl":"10.1016/j.nonrwa.2026.104610","url":null,"abstract":"<div><div>The present paper discusses the dynamics and optimal harvesting of an intraguild predation three-level food web model incorporating nonlinear Michaelis-Menten type harvesting on the intermediate predator and proportional harvesting on the intraguild predator. The positivity and boundedness of solutions, as well as the existence and stability of equilibria, are established, and unconditional survival of the prey species is observed. The effect of harvesting is studied through a detailed bifurcation analysis, revealing rich dynamical behaviors and threshold harvesting levels that prevent predator extinction. The existence of saddle-node, transcritical, pitchfork, and Hopf bifurcations is shown. The qualitative dynamics are discussed through two-parameter bifurcation diagram. Parameter regions of extinction and coexistence are identified. At higher harvesting rates, Bogdanov-Takens and generalized Hopf bifurcations reveal parametric regions in which either both predator species will eventually be driven to extinction or all three species may coexist, depending on the initial values. At lower harvesting rates, Zero-Hopf and generalized Hopf bifurcations reveal parametric regions in which either intermediate predator eventually goes extinct or all three species may coexist, depending on the initial population densities. It is shown that the system can exhibit multistability and sensitivity to initial conditions, with bistability between coexistence attractors and predator-free attractors. From an economic perspective, an optimal harvesting policy is derived, maximizing the total economic return from harvesting while preventing overharvesting and ensuring ecological sustainability. A numerical example shows that both economic benefits and ecological balance can be achieved by controlling both predators harvesting rates.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104610"},"PeriodicalIF":1.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077471","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 : 2026-01-29DOI: 10.1016/j.nonrwa.2026.104608
Minjiang Feng, Sirui Li, Qi Zeng
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution equation of the orthonormal frame field and the Navier–Stokes equation of the fluid velocity field, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish the global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on the estimates of nonlinear terms with the rotational derivative on SO(3), together with the dissipative structure of the frame hydrodynamics.
{"title":"Global strong solutions to the frame hydrodynamics for biaxial nematic phases","authors":"Minjiang Feng, Sirui Li, Qi Zeng","doi":"10.1016/j.nonrwa.2026.104608","DOIUrl":"10.1016/j.nonrwa.2026.104608","url":null,"abstract":"<div><div>In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution equation of the orthonormal frame field and the Navier–Stokes equation of the fluid velocity field, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish the global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on the estimates of nonlinear terms with the rotational derivative on <em>SO</em>(3), together with the dissipative structure of the frame hydrodynamics.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104608"},"PeriodicalIF":1.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077473","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 : 2026-01-28DOI: 10.1016/j.nonrwa.2026.104609
Pascal Lehner
We study well-posedness of a first-order-in-time model for nonlinear acoustics with nonhomogeneous boundary conditions in fractional Sobolev spaces. The analysis proceeds by first establishing well-posedness of an abstract parabolic-type semilinear evolution equation. These results are then applied to concrete operators and function spaces that capture the boundary conditions relevant for realistic modeling.
Our approach is based on the spectral decomposition of a positive definite self-adjoint operator, with solution regularity characterized via the domains of its fractional powers. Employing Galerkin’s method and the Newton-Kantorovich theorem, we prove well-posedness for the abstract nonlinear system with possibly nonhomogeneous boundary data.
The connection between (spectral) fractional powers of the Laplacian and fractional Sobolev spaces due to interpolation theory allows us to transfer these results to the nonlinear acoustic model under nonhomogeneous Dirichlet and Neumann boundary conditions, yielding fractional Sobolev regularity. For Hodge/Lions boundary conditions, we establish well-posedness with solutions in classical Sobolev spaces of integer order.
{"title":"Well-posedness of a first-order-in-time model for nonlinear acoustics with nonhomogeneous boundary conditions","authors":"Pascal Lehner","doi":"10.1016/j.nonrwa.2026.104609","DOIUrl":"10.1016/j.nonrwa.2026.104609","url":null,"abstract":"<div><div>We study well-posedness of a first-order-in-time model for nonlinear acoustics with nonhomogeneous boundary conditions in fractional Sobolev spaces. The analysis proceeds by first establishing well-posedness of an abstract parabolic-type semilinear evolution equation. These results are then applied to concrete operators and function spaces that capture the boundary conditions relevant for realistic modeling.</div><div>Our approach is based on the spectral decomposition of a positive definite self-adjoint operator, with solution regularity characterized via the domains of its fractional powers. Employing Galerkin’s method and the Newton-Kantorovich theorem, we prove well-posedness for the abstract nonlinear system with possibly nonhomogeneous boundary data.</div><div>The connection between (spectral) fractional powers of the Laplacian and fractional Sobolev spaces due to interpolation theory allows us to transfer these results to the nonlinear acoustic model under nonhomogeneous Dirichlet and Neumann boundary conditions, yielding fractional Sobolev regularity. For Hodge/Lions boundary conditions, we establish well-posedness with solutions in classical Sobolev spaces of integer order.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104609"},"PeriodicalIF":1.8,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077470","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 : 2026-01-27DOI: 10.1016/j.nonrwa.2026.104606
Chun Wu
This paper deals with the following quasilinear chemotaxis systemunder the homogeneous Neumann boundary condition in with smooth boundary ∂Ω, where the parameters a, b > 0 and m > 1. It is shown that there is at least one global weak solution for the system being discussed.
{"title":"Global existence of weak solutions to a quasilinear parabolic chemotaxis system","authors":"Chun Wu","doi":"10.1016/j.nonrwa.2026.104606","DOIUrl":"10.1016/j.nonrwa.2026.104606","url":null,"abstract":"<div><div>This paper deals with the following quasilinear chemotaxis system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>∇</mi><msup><mi>u</mi><mi>m</mi></msup><mo>−</mo><mi>u</mi><mi>v</mi><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>u</mi><mo>−</mo><mi>b</mi><msup><mi>u</mi><mn>2</mn></msup><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>v</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mtd></mtr></mtable></mrow></math></span></span></span>under the homogeneous Neumann boundary condition in <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mi>n</mi></msup><mspace></mspace><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary ∂Ω, where the parameters <em>a, b</em> > 0 and <em>m</em> > 1. It is shown that there is at least one global weak solution for the system being discussed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104606"},"PeriodicalIF":1.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077472","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 : 2026-01-22DOI: 10.1016/j.nonrwa.2026.104604
Kh Zennir , S. Bousserhane Reda , T. Miyasita , S.G. Georgiev , K. Bouhali
The study of finite-time blow-up of solutions for coupled systems is a complex and intriguing topic in the theory of partial differential equations, especially when the coupling comes from nonlinear memory sources. This area concerns understanding when the local solutions may “blow up”, meaning they become unbounded in a finite time. The purpose of this study is to use the proof by contradiction to show the finite-time blow-up of solutions for the problem of coupled nonlinear waves in the structural damped model with nonlinear memory sources under certain regularity properties and conditions on the exponents.
{"title":"Finite time blow up of solutions for coupled system of wave equations with nonlinear memory terms","authors":"Kh Zennir , S. Bousserhane Reda , T. Miyasita , S.G. Georgiev , K. Bouhali","doi":"10.1016/j.nonrwa.2026.104604","DOIUrl":"10.1016/j.nonrwa.2026.104604","url":null,"abstract":"<div><div>The study of finite-time blow-up of solutions for coupled systems is a complex and intriguing topic in the theory of partial differential equations, especially when the coupling comes from nonlinear memory sources. This area concerns understanding when the local solutions may “blow up”, meaning they become unbounded in a finite time. The purpose of this study is to use the proof by contradiction to show the finite-time blow-up of solutions for the problem of coupled nonlinear waves in the structural damped model with nonlinear memory sources under certain regularity properties and conditions on the exponents.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104604"},"PeriodicalIF":1.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037632","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 : 2026-01-21DOI: 10.1016/j.nonrwa.2026.104602
Meina Sun
The Riemann solutions for the simplified liquid-gas two-phase modified Chaplygin flow model are obtained constructively by virtue of the equality of velocity and pressure across the second characteristic field. Then, we are mainly concerned with the transition of Riemann solutions for this model when the equation of state varies from the modified Chaplygin flow to the Chaplygin flow by letting the perturbed parameter drop to zero. The formation of delta shock Riemann solution for the Chaplygin flow model is explored carefully by sending the limit in the Riemann solution made up of first-shock wave, second-contact discontinuity and third-shock wave for the modified Chaplygin flow model. In addition, the formation of the association of three contact discontinuities for the Chaplygin flow model is also carried out by taking the limit in all the four different structural Riemann solutions for the modified Chaplygin flow model.
{"title":"The transition of Riemann solutions for a simplified liquid-gas two-phase modified Chaplygin flow model","authors":"Meina Sun","doi":"10.1016/j.nonrwa.2026.104602","DOIUrl":"10.1016/j.nonrwa.2026.104602","url":null,"abstract":"<div><div>The Riemann solutions for the simplified liquid-gas two-phase modified Chaplygin flow model are obtained constructively by virtue of the equality of velocity and pressure across the second characteristic field. Then, we are mainly concerned with the transition of Riemann solutions for this model when the equation of state varies from the modified Chaplygin flow to the Chaplygin flow by letting the perturbed parameter drop to zero. The formation of delta shock Riemann solution for the Chaplygin flow model is explored carefully by sending the limit in the Riemann solution made up of first-shock wave, second-contact discontinuity and third-shock wave for the modified Chaplygin flow model. In addition, the formation of the association of three contact discontinuities for the Chaplygin flow model is also carried out by taking the limit in all the four different structural Riemann solutions for the modified Chaplygin flow model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104602"},"PeriodicalIF":1.8,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037631","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 : 2026-01-20DOI: 10.1016/j.nonrwa.2026.104601
Lennon Ó Náraigh , Khang Ee Pang , Richard J. Smith
The Geometric Thin-Film Equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. We show that the weak formulation of the problem, given initial Radon data, admits solutions that are globally defined for all time and are expressible as push-forwards of Borel measurable functions whose behaviour is governed by a set of ordinary differential equations (ODEs). The existence is first demonstrated in the special case of a finite weighted sum of delta functions whose centres evolve over time – these are known as ‘particle solutions’. In the general case, we construct a convergent sequence of particle solutions whose limit yields a solution of the above form. Moreover, we demonstrate that all weak solutions constructed in this way are 1/2-Hölder continuous in time and are uniquely determined by the initial conditions.
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