Pub Date : 2025-10-18DOI: 10.1016/j.aml.2025.109790
Yunjuan Jin , Zehua Wu , Huiling Wu
An extended Benjamin–Ono equation with the Hilbert transform is proposed and its bilinear form is presented explicitly. Based on this bilinear equation, multi-periodic wave solutions are obtained via the perturbation technique. By taking a long wave limit on these periodic wave solutions, soliton solutions and mixed solutions representing the interaction between solitons and periodic waves are further derived. The dynamic behaviors of these solutions are visually illustrated through numerical plots.
{"title":"Periodic wave, soliton and mixed solutions for an extended Benjamin–Ono equation","authors":"Yunjuan Jin , Zehua Wu , Huiling Wu","doi":"10.1016/j.aml.2025.109790","DOIUrl":"10.1016/j.aml.2025.109790","url":null,"abstract":"<div><div>An extended Benjamin–Ono equation with the Hilbert transform is proposed and its bilinear form is presented explicitly. Based on this bilinear equation, multi-periodic wave solutions are obtained via the perturbation technique. By taking a long wave limit on these periodic wave solutions, soliton solutions and mixed solutions representing the interaction between solitons and periodic waves are further derived. The dynamic behaviors of these solutions are visually illustrated through numerical plots.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109790"},"PeriodicalIF":2.8,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-11DOI: 10.1016/j.aml.2025.109788
Hui Kang , Tianfang Wang , Wen Zhang
In this paper, we investigate a class of asymptotically quadratic Dirac–Bopp–Podolsky system in relativistic quantum electrodynamics. As we know that the Dirac operator is unbounded from below and above, then the associated energy functional is strongly indefinite. Applying the multiple critical point theorem of strongly indefinite functionals and concentration compactness arguments, we establish the existence and multiplicity result of nontrivial solutions.
{"title":"Existence and multiplicity of solutions for a class of nonlinear Dirac–Bopp–Podolsky system","authors":"Hui Kang , Tianfang Wang , Wen Zhang","doi":"10.1016/j.aml.2025.109788","DOIUrl":"10.1016/j.aml.2025.109788","url":null,"abstract":"<div><div>In this paper, we investigate a class of asymptotically quadratic Dirac–Bopp–Podolsky system in relativistic quantum electrodynamics. As we know that the Dirac operator is unbounded from below and above, then the associated energy functional is strongly indefinite. Applying the multiple critical point theorem of strongly indefinite functionals and concentration compactness arguments, we establish the existence and multiplicity result of nontrivial solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109788"},"PeriodicalIF":2.8,"publicationDate":"2025-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-11DOI: 10.1016/j.aml.2025.109789
Xiaopeng Lian , Xinyao Liu , Minqiang Xu
This paper presents an efficient and stable fully discrete numerical scheme for Korteweg–de Vries (KdV) equations. The novel scheme combines finite element (FE) methods for the spatial discretization with the corresponding time-stepping Petrov–Galerkin (PG) method for the temporal discretization. Specifically, the variational formulation of KdV equations is derived under the PG framework. A key component of our approach involves using a Hessian recovery operator to accurately compute the second derivative of the finite element function; We also provide a theoretical proof that the fully discrete Petrov–Galerkin time-stepping scheme, combined with the Hessian recovery finite element method, exactly preserves momentum and energy. We also theoretically prove that the fully discrete Petrov–Galerkin time-stepping scheme, combined with the Hessian recovery finite element method(PG-HRFEM), exactly preserves momentum energy. Numerical experiments confirm optimal error estimates in both the and the norms, and reveal superconvergence in the error norms of the recovered and space. Long-time simulations further show the presented method effectively preserves and efficiently maintains solution phase shape over extended periods.
{"title":"An efficient and stable C0 finite element methods for Korteweg–de Vries equations","authors":"Xiaopeng Lian , Xinyao Liu , Minqiang Xu","doi":"10.1016/j.aml.2025.109789","DOIUrl":"10.1016/j.aml.2025.109789","url":null,"abstract":"<div><div>This paper presents an efficient and stable fully discrete numerical scheme for Korteweg–de Vries (KdV) equations. The novel scheme combines <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> finite element (FE) methods for the spatial discretization with the corresponding time-stepping Petrov–Galerkin (PG) method for the temporal discretization. Specifically, the variational formulation of KdV equations is derived under the PG framework. A key component of our approach involves using a Hessian recovery operator to accurately compute the second derivative of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> finite element function; We also provide a theoretical proof that the fully discrete Petrov–Galerkin time-stepping scheme, combined with the Hessian recovery finite element method, exactly preserves momentum and energy. We also theoretically prove that the fully discrete Petrov–Galerkin time-stepping scheme, combined with the Hessian recovery finite element method(PG-HRFEM), exactly preserves momentum energy. Numerical experiments confirm optimal error estimates in both the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms, and reveal superconvergence in the error norms of the recovered <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> space. Long-time simulations further show the presented method effectively preserves <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and efficiently maintains solution phase shape over extended periods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109789"},"PeriodicalIF":2.8,"publicationDate":"2025-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-10DOI: 10.1016/j.aml.2025.109787
Jian Liu
This paper establishes the existence and uniqueness of weak solutions for a class of double-degenerate singular elliptic equations involving -Laplacian operator with weight functions and and a gradient-dependent nonlinearity. We introduce a novel weighted boundedness condition based on to handle singular coefficients and relax regularity requirements. To the best of our knowledge, such conditions have not been previously addressed in the literature. Working in the weighted Sobolev space , we prove the associated operator is bounded, coercive, semicontinuous, and strictly monotone. Applying the Minty–Browder theorem, we obtain an explicit parameter range for ensuring a unique weak solution.
{"title":"Degenerate (p,r)-Laplacian elliptic equations under weighted boundedness conditions","authors":"Jian Liu","doi":"10.1016/j.aml.2025.109787","DOIUrl":"10.1016/j.aml.2025.109787","url":null,"abstract":"<div><div>This paper establishes the existence and uniqueness of weak solutions for a class of double-degenerate singular elliptic equations involving <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo>)</mo></mrow></math></span>-Laplacian operator with weight functions <span><math><mrow><mi>ω</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>ϑ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and a gradient-dependent nonlinearity. We introduce a novel weighted boundedness condition based on <span><math><mrow><mi>ω</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> to handle singular coefficients and relax regularity requirements. To the best of our knowledge, such conditions have not been previously addressed in the literature. Working in the weighted Sobolev space <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, we prove the associated operator is bounded, coercive, semicontinuous, and strictly monotone. Applying the Minty–Browder theorem, we obtain an explicit parameter range for <span><math><mi>λ</mi></math></span> ensuring a unique weak solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109787"},"PeriodicalIF":2.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-10DOI: 10.1016/j.aml.2025.109786
Salim Yüce
Correspondence between points on the dual unit sphere and lines in the Euclidean space was first expressed in E. Study Maps, which has served as the foundation for numerous studies in the theory of ruled surfaces and kinematics. The enduring legacy of this theorem lies in the correspondence it establishes between the curves on the dual unit sphere and the ruled surfaces in . Yet, it has prompted fixation on the dual unit sphere, leading to the neglect of the broader and leaving the theory of curves, surface theory and kinematics in largely unexplored. To fill this gap, the present study introduces “generalized E. Study Maps” that proves that for every dual curve in , there exists a corresponding ruled surface in . Furthermore, the study constructs the theory of curves in via theory of real curves. The study is expected to guide future research on the dual curve theory, dual surface theory and kinematics in , and pave the way for exploring the magical correspondence between and from an expanded viewpoint.
对偶单位球面上的点与欧几里得空间R3中直线的对应关系首先在E. Study Maps中表达出来，它成为了许多直纹曲面理论和运动学研究的基础。这个定理的不朽遗产在于它建立了对偶单位球面上的曲线与R3中的直纹曲面之间的对应关系。然而，它引起了对偶单位球的固定，导致忽略了更广泛的D3，并使D3中的曲线理论，曲面理论和运动学在很大程度上未被探索。为了填补这一空白，本研究引入了“generalized E. study Maps”，证明对于D3中的每一条对偶曲线，在R3中存在一个对应的直纹曲面。进一步，通过实曲线理论构建了D3中的曲线理论。该研究有望指导未来对D3中的对偶曲线理论、对偶曲面理论和运动学的研究，并为从扩展的角度探索D3与R3之间的神奇对应关系铺平道路。
{"title":"Innovations beyond the Classical Framework in the Dual Space D3","authors":"Salim Yüce","doi":"10.1016/j.aml.2025.109786","DOIUrl":"10.1016/j.aml.2025.109786","url":null,"abstract":"<div><div>Correspondence between points on the dual unit sphere and lines in the Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> was first expressed in E. Study Maps, which has served as the foundation for numerous studies in the theory of ruled surfaces and kinematics. The enduring legacy of this theorem lies in the correspondence it establishes between the curves on the dual unit sphere and the ruled surfaces in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Yet, it has prompted fixation on the dual unit sphere, leading to the neglect of the broader <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and leaving the theory of curves, surface theory and kinematics in <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> largely unexplored. To fill this gap, the present study introduces “generalized E. Study Maps” that proves that for every dual curve in <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, there exists a corresponding ruled surface in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Furthermore, the study constructs the theory of curves in <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> via theory of real curves. The study is expected to guide future research on the dual curve theory, dual surface theory and kinematics in <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, and pave the way for exploring the magical correspondence between <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> from an expanded viewpoint.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109786"},"PeriodicalIF":2.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-10DOI: 10.1016/j.aml.2025.109785
Chaitanya Gopalakrishna , Weinian Zhang
The existence of increasing convex continuous solutions to polynomial-like iterative equations on compact intervals was investigated in Zhang et al. (2006) and Xu and Zhang (2007) using the Schauder fixed point theorem and the Banach contraction principle; however, all of those results were proved under the severe assumption that the given function is a Lipschitzian map on its domain. In this paper we investigate their convex solutions with a weaker regularity, avoiding the Lipschitz requirement. Using the Knaster–Tarski fixed point theorem, we provide sufficient conditions for the existence of increasing convex semi-continuous solutions to these equations with no Lipschitz assumption on the given function. In particular, this fixed point theorem allows us to deduce further structure of the sets of such solutions to these equations, showing that they are complete lattices and thus proving the existence of minimum and maximum solutions to these equations rather than just the existence or uniqueness of solutions, as proved using the above fixed point theorems.
Zhang et al.（2006）和Xu and Zhang（2007）利用Schauder不动点定理和Banach收缩原理研究了紧区间上类多项式迭代方程凸渐增连续解的存在性；然而，所有这些结果都是在一个严格的假设下证明的，即给定函数是其定义域上的Lipschitzian映射。本文研究了它们的凸解具有较弱的正则性，避免了Lipschitz条件。利用Knaster-Tarski不动点定理，给出了这些方程在给定函数没有Lipschitz假设的情况下凸渐增半连续解存在的充分条件。特别地，这个不动点定理使我们能够进一步推导出这些方程解的集合的结构，表明它们是完全格，从而证明了这些方程的最小解和最大解的存在性，而不是像用上述不动点定理证明的那样仅仅是解的存在性或唯一性。
{"title":"Convex semi-continuous solutions of polynomial-like iterative equations","authors":"Chaitanya Gopalakrishna , Weinian Zhang","doi":"10.1016/j.aml.2025.109785","DOIUrl":"10.1016/j.aml.2025.109785","url":null,"abstract":"<div><div>The existence of increasing convex continuous solutions to polynomial-like iterative equations on compact intervals was investigated in Zhang et al. (2006) and Xu and Zhang (2007) using the Schauder fixed point theorem and the Banach contraction principle; however, all of those results were proved under the severe assumption that the given function is a Lipschitzian map on its domain. In this paper we investigate their convex solutions with a weaker regularity, avoiding the Lipschitz requirement. Using the Knaster–Tarski fixed point theorem, we provide sufficient conditions for the existence of increasing convex semi-continuous solutions to these equations with no Lipschitz assumption on the given function. In particular, this fixed point theorem allows us to deduce further structure of the sets of such solutions to these equations, showing that they are complete lattices and thus proving the existence of minimum and maximum solutions to these equations rather than just the existence or uniqueness of solutions, as proved using the above fixed point theorems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109785"},"PeriodicalIF":2.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-09DOI: 10.1016/j.aml.2025.109782
Ying Chao , Jinqiao Duan , Pingyuan Wei
We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.
{"title":"Most probable escape paths in perturbed kinetic Langevin systems","authors":"Ying Chao , Jinqiao Duan , Pingyuan Wei","doi":"10.1016/j.aml.2025.109782","DOIUrl":"10.1016/j.aml.2025.109782","url":null,"abstract":"<div><div>We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109782"},"PeriodicalIF":2.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-08DOI: 10.1016/j.aml.2025.109783
Yuanyuan Xu, Shuyang Xue
In this paper, we investigate the spatiotemporal dynamics in the nonlocal advection–diffusion equation with delay. The nonlocal advection is characterized by the top-hat kernel and time delay measures the delay phenomenon in the reaction term. The joint effect of the nonlocal advection and delay on the stability of the steady state and spatiotemporal dynamics is investigated. The conditions for the occurrence of Turing bifurcation and Turing–Hopf bifurcation are determined. Our results show that the large perception range can stabilize the steady state, but a small perception range is more likely to make the system unstable, and negative feedback of delay is more easy to make system produce complex patterns. It has also been shown that spatially inhomogeneous oscillatory patterns are triggered by the joint interaction of nonlocal advection and delay, which can not occur only for one factor.
{"title":"Spatiotemporal patterns driven by the nonlocal advection and delay","authors":"Yuanyuan Xu, Shuyang Xue","doi":"10.1016/j.aml.2025.109783","DOIUrl":"10.1016/j.aml.2025.109783","url":null,"abstract":"<div><div>In this paper, we investigate the spatiotemporal dynamics in the nonlocal advection–diffusion equation with delay. The nonlocal advection is characterized by the top-hat kernel and time delay measures the delay phenomenon in the reaction term. The joint effect of the nonlocal advection and delay on the stability of the steady state and spatiotemporal dynamics is investigated. The conditions for the occurrence of Turing bifurcation and Turing–Hopf bifurcation are determined. Our results show that the large perception range can stabilize the steady state, but a small perception range is more likely to make the system unstable, and negative feedback of delay is more easy to make system produce complex patterns. It has also been shown that spatially inhomogeneous oscillatory patterns are triggered by the joint interaction of nonlocal advection and delay, which can not occur only for one factor.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109783"},"PeriodicalIF":2.8,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-05DOI: 10.1016/j.aml.2025.109781
Lin Liu , Baoting Su , Hongqing Song , Libo Feng
As a mathematical tool for addressing problems in unbounded domains, the absorbing boundary conditions derived by artificial boundary method are widely used in various scientific fields. This study mainly investigates the hydrodynamic behavior of Walter’s-B fluid over an inclined plate. Considering the effects of chemical reactions as well as the heat absorption/generation, the governing model is derived. By employing the -transform, the governing Eqs. defined in an unbounded domain are transformed into a computationally tractable finite domain, for which the finite difference method is applied. Numerical simulations are conducted to analyze the influence of various dimensionless parameters. Finally, a quantitative physical analysis is performed to evaluate the impact of these parameters on the concentration profile, temperature distribution, and velocity field.
{"title":"Numerical simulation of heat transfer and flow characteristics of Walter’s-B fluid over an inclined plate in a semi-infinite magnetic field","authors":"Lin Liu , Baoting Su , Hongqing Song , Libo Feng","doi":"10.1016/j.aml.2025.109781","DOIUrl":"10.1016/j.aml.2025.109781","url":null,"abstract":"<div><div>As a mathematical tool for addressing problems in unbounded domains, the absorbing boundary conditions derived by artificial boundary method are widely used in various scientific fields. This study mainly investigates the hydrodynamic behavior of Walter’s-B fluid over an inclined plate. Considering the effects of chemical reactions as well as the heat absorption/generation, the governing model is derived. By employing the <span><math><mi>z</mi></math></span>-transform, the governing Eqs. defined in an unbounded domain are transformed into a computationally tractable finite domain, for which the finite difference method is applied. Numerical simulations are conducted to analyze the influence of various dimensionless parameters. Finally, a quantitative physical analysis is performed to evaluate the impact of these parameters on the concentration profile, temperature distribution, and velocity field.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109781"},"PeriodicalIF":2.8,"publicationDate":"2025-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-04DOI: 10.1016/j.aml.2025.109784
Patrick Buchfink , Silke Glas , Hans Zwart
We combine energy-stable and port-Hamiltonian (pH) systems to obtain energy-stable port-Hamiltonian (es-pH) systems. The idea is to extend the known energy-stable systems with an input–output port, which results in a pH formulation. One advantage of the new es-pH formulation is that it naturally preserves its es-pH structure throughout discretization (in space and time) and model reduction.
{"title":"Energy-stable port-Hamiltonian systems","authors":"Patrick Buchfink , Silke Glas , Hans Zwart","doi":"10.1016/j.aml.2025.109784","DOIUrl":"10.1016/j.aml.2025.109784","url":null,"abstract":"<div><div>We combine energy-stable and port-Hamiltonian (<span>pH</span>) systems to obtain <em>energy-stable port-Hamiltonian (<span>es-pH</span>) systems</em>. The idea is to extend the known energy-stable systems with an input–output port, which results in a <span>pH</span> formulation. One advantage of the new <span>es-pH</span> formulation is that it naturally preserves its <span>es-pH</span> structure throughout discretization (in space and time) and model reduction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109784"},"PeriodicalIF":2.8,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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