Pub Date : 2025-10-30DOI: 10.1016/j.aml.2025.109797
Jiangfeng Han , Zhao Jing , Zhenhai Liu
This paper investigates damped elastic inclusion systems subjected to nonconvex-valued perturbations. Our primary contribution lies in establishing an existence theorem for mild solutions under suitable regularity conditions. To illustrate the practical applicability of these abstract findings, we conduct an explicit analysis of solutions in elastic feedback control systems.
{"title":"Existence of solutions for damped elastic inclusions with nonconvex-valued perturbations","authors":"Jiangfeng Han , Zhao Jing , Zhenhai Liu","doi":"10.1016/j.aml.2025.109797","DOIUrl":"10.1016/j.aml.2025.109797","url":null,"abstract":"<div><div>This paper investigates damped elastic inclusion systems subjected to nonconvex-valued perturbations. Our primary contribution lies in establishing an existence theorem for mild solutions under suitable regularity conditions. To illustrate the practical applicability of these abstract findings, we conduct an explicit analysis of solutions in elastic feedback control systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109797"},"PeriodicalIF":2.8,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382493","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 : 2025-10-30DOI: 10.1016/j.aml.2025.109805
Tingting Wu , Jiayuan Liu
In this paper, a fourth-order finite difference scheme is proposed to solve the exterior Helmholtz problem in polar coordinates. The perfectly matched layer (PML) technique is applied to truncate the unbounded domain into a bounded domain, and absorb the outgoing waves. Using the undetermined coefficient method, a fourth-order finite difference scheme for the Helmholtz equation with PML in polar coordinates is established. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed scheme.
{"title":"A fourth-order scheme for the exterior Helmholtz problem in polar coordinates","authors":"Tingting Wu , Jiayuan Liu","doi":"10.1016/j.aml.2025.109805","DOIUrl":"10.1016/j.aml.2025.109805","url":null,"abstract":"<div><div>In this paper, a fourth-order finite difference scheme is proposed to solve the exterior Helmholtz problem in polar coordinates. The perfectly matched layer (PML) technique is applied to truncate the unbounded domain into a bounded domain, and absorb the outgoing waves. Using the undetermined coefficient method, a fourth-order finite difference scheme for the Helmholtz equation with PML in polar coordinates is established. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"174 ","pages":"Article 109805"},"PeriodicalIF":2.8,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145396742","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}
{"title":"Retraction notice to “Analysis on the motion of nonlinear vibration with fractional order and time variable mass” [Appl. Math. Lett. 124 (2022) 107621]","authors":"Yue Yu , Wenyao Zhou , Zhengdi Zhang , Qinsheng Bi","doi":"10.1016/j.aml.2025.109792","DOIUrl":"10.1016/j.aml.2025.109792","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109792"},"PeriodicalIF":2.8,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145396749","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 : 2025-10-29DOI: 10.1016/j.aml.2025.109802
Mingxi Li, Qian Zhang
We study the Cauchy problem for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion . Leveraging the axisymmetric non-swirl flow structure, we extend the range of to and prove the global existence of weak solutions for this model. Besides we extend the global result from bounded domain (Winkler, 2015) to the entire spaces.
{"title":"On the global existence of weak solution for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion","authors":"Mingxi Li, Qian Zhang","doi":"10.1016/j.aml.2025.109802","DOIUrl":"10.1016/j.aml.2025.109802","url":null,"abstract":"<div><div>We study the Cauchy problem for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion <span><math><mrow><mi>Δ</mi><msup><mrow><mi>n</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>. Leveraging the axisymmetric non-swirl flow structure, we extend the range of <span><math><mi>m</mi></math></span> to <span><math><mrow><mo>(</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> and prove the global existence of weak solutions for this model. Besides we extend the global result from bounded domain (Winkler, 2015) to the entire spaces.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109802"},"PeriodicalIF":2.8,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382495","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 : 2025-10-28DOI: 10.1016/j.aml.2025.109801
Salim Yüce
{"title":"Withdrawal notice to: “Innovations beyond the Classical Framework in the Dual Space D3” [Appl. Math. Lett. 173 (2026) 109786]","authors":"Salim Yüce","doi":"10.1016/j.aml.2025.109801","DOIUrl":"10.1016/j.aml.2025.109801","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109801"},"PeriodicalIF":2.8,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382496","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 : 2025-10-28DOI: 10.1016/j.aml.2025.109803
Bo Gong , Takumi Sato , Jiguang Sun , Xinming Wu
The study of resonances of the Schrödinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds on the counting functions. However, computational results beyond one dimension remain scarce due to the nonlinearity of the problem and the unbounded nature of the domain. We propose a novel approach that integrates finite elements, Dirichlet-to-Neumann (DtN) mapping, and the spectral indicator method. The DtN mapping, imposed on the boundary of a truncated computational domain, enforces the outgoing condition. Finite elements allow for the efficient handling of complicated potential functions. Finally, the spectral indicator method is employed to compute (complex) eigenvalues of the resulting nonlinear algebraic system. The viability of this approach is demonstrated through a range of numerical examples.
{"title":"FEM-DtN-SIM method for computing resonances of Schrödinger operators","authors":"Bo Gong , Takumi Sato , Jiguang Sun , Xinming Wu","doi":"10.1016/j.aml.2025.109803","DOIUrl":"10.1016/j.aml.2025.109803","url":null,"abstract":"<div><div>The study of resonances of the Schrödinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds on the counting functions. However, computational results beyond one dimension remain scarce due to the nonlinearity of the problem and the unbounded nature of the domain. We propose a novel approach that integrates finite elements, Dirichlet-to-Neumann (DtN) mapping, and the spectral indicator method. The DtN mapping, imposed on the boundary of a truncated computational domain, enforces the outgoing condition. Finite elements allow for the efficient handling of complicated potential functions. Finally, the spectral indicator method is employed to compute (complex) eigenvalues of the resulting nonlinear algebraic system. The viability of this approach is demonstrated through a range of numerical examples.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109803"},"PeriodicalIF":2.8,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145396449","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 : 2025-10-24DOI: 10.1016/j.aml.2025.109800
Jian Xu , Ning Guo
The rogue wave solutions of the focusing Hirota equation are usually obtained via the Darboux transformation or the bilinear method. In this paper, however, we derive these solutions under nonzero boundary conditions by employing a limiting technique applied at the branch point of the spectral parameter, based on the Riemann–Hilbert problem formulation. Furthermore, we demonstrate that the N-double-pole solutions can be generated by taking appropriate limits of the corresponding simple-pole soliton solutions with nonzero boundary conditions.
{"title":"On the Riemann–Hilbert problem method to rogue wave solution of the focusing Hirota equation","authors":"Jian Xu , Ning Guo","doi":"10.1016/j.aml.2025.109800","DOIUrl":"10.1016/j.aml.2025.109800","url":null,"abstract":"<div><div>The rogue wave solutions of the focusing Hirota equation are usually obtained via the Darboux transformation or the bilinear method. In this paper, however, we derive these solutions under nonzero boundary conditions by employing a limiting technique applied at the branch point of the spectral parameter, based on the Riemann–Hilbert problem formulation. Furthermore, we demonstrate that the N-double-pole solutions can be generated by taking appropriate limits of the corresponding simple-pole soliton solutions with nonzero boundary conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109800"},"PeriodicalIF":2.8,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363330","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 : 2025-10-24DOI: 10.1016/j.aml.2025.109798
Li Chai, Yang Liu, Hong Li
Two families of weighted- compact alternating direction implicit (ADI) difference methods are developed to solve three-dimensional space fractional complex Ginzburg–Landau (3DSFCGL) equation. The article focuses primarily on the high-accuracy and computational efficiency of the constructed methods. To this end, the compact ADI difference schemes are introduced. By a combination of two families of weighted- methods and the compact ADI difference method, the fully discrete scheme is designed, and the corresponding theoretical results are presented. Finally, numerical tests are carried out to demonstrate the feasibility of our schemes and to simulate the dynamic diffusion behavior of the wave function.
{"title":"Two families of weighted-θ compact ADI difference schemes for the three-dimensional space fractional complex Ginzburg–Landau equation","authors":"Li Chai, Yang Liu, Hong Li","doi":"10.1016/j.aml.2025.109798","DOIUrl":"10.1016/j.aml.2025.109798","url":null,"abstract":"<div><div>Two families of weighted-<span><math><mi>θ</mi></math></span> compact alternating direction implicit (ADI) difference methods are developed to solve three-dimensional space fractional complex Ginzburg–Landau (3DSFCGL) equation. The article focuses primarily on the high-accuracy and computational efficiency of the constructed methods. To this end, the compact ADI difference schemes are introduced. By a combination of two families of weighted-<span><math><mi>θ</mi></math></span> methods and the compact ADI difference method, the fully discrete scheme is designed, and the corresponding theoretical results are presented. Finally, numerical tests are carried out to demonstrate the feasibility of our schemes and to simulate the dynamic diffusion behavior of the wave function.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109798"},"PeriodicalIF":2.8,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382518","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 : 2025-10-23DOI: 10.1016/j.aml.2025.109799
Qingyang Yuan, Guangying Lv
This paper is concerned with the preservation of concave property of delayed parabolic system. By introducing new variable, we translate the delayed parabolic system into a parabolic system without delay. Then by using the comparison principle, we obtain the preservation of concavity of parabolic system.
{"title":"Preservation of geometry property of delayed parabolic equations","authors":"Qingyang Yuan, Guangying Lv","doi":"10.1016/j.aml.2025.109799","DOIUrl":"10.1016/j.aml.2025.109799","url":null,"abstract":"<div><div>This paper is concerned with the preservation of concave property of delayed parabolic system. By introducing new variable, we translate the delayed parabolic system into a parabolic system without delay. Then by using the comparison principle, we obtain the preservation of concavity of parabolic system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109799"},"PeriodicalIF":2.8,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363329","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 : 2025-10-22DOI: 10.1016/j.aml.2025.109795
Renjie Xu , Wanli Ma , Maolin Che
In this article, we investigate the asymptotic stability of the system of third-order quaternion-tensor delay differential equations. Sufficient conditions for stability are established based on the T-product algebra, using both the quaternion logarithmic norm and numerical radius. A numerical example is provided to illustrate the effectiveness of the proposed criteria.
{"title":"Numerical radius approach to asymptotic stability of quaternion-tensor delay systems","authors":"Renjie Xu , Wanli Ma , Maolin Che","doi":"10.1016/j.aml.2025.109795","DOIUrl":"10.1016/j.aml.2025.109795","url":null,"abstract":"<div><div>In this article, we investigate the asymptotic stability of the system of third-order quaternion-tensor delay differential equations. Sufficient conditions for stability are established based on the T-product algebra, using both the quaternion logarithmic norm and numerical radius. A numerical example is provided to illustrate the effectiveness of the proposed criteria.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109795"},"PeriodicalIF":2.8,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362321","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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