Pub Date : 2025-12-26DOI: 10.1016/j.aml.2025.109857
Minh-Phuong Tran , Thanh-Nhan Nguyen
We study the regularity of solutions to nonlinear elliptic equations of -Laplace type modeled from composite materials. The main difficulty comes from the geometric structures of the composite, specifically the disjoint Reifenberg flat subdomains , their boundaries , and the BMO smallness properties of each tensor coefficient that pose significant challenges. In this paper, we develop a novel free-scaling approach to establish the local decay estimates for level sets of the gradient of the weak solutions. This approach is of independent technical interest, and it is flexible enough to be applied for deriving improved gradient regularity in a larger class of rearrangement-invariant function spaces.
{"title":"Global Marcinkiewicz estimates for p-Laplace equations in composite media: A new free-scaling approach via distribution functions","authors":"Minh-Phuong Tran , Thanh-Nhan Nguyen","doi":"10.1016/j.aml.2025.109857","DOIUrl":"10.1016/j.aml.2025.109857","url":null,"abstract":"<div><div>We study the regularity of solutions to nonlinear elliptic equations of <span><math><mi>p</mi></math></span>-Laplace type modeled from composite materials. The main difficulty comes from the geometric structures of the composite, specifically the disjoint Reifenberg flat subdomains <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, their boundaries <span><math><mrow><mi>∂</mi><msub><mrow><mi>Ω</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></math></span>, and the BMO smallness properties of each tensor coefficient <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> that pose significant challenges. In this paper, we develop a novel free-scaling approach to establish the local decay estimates for level sets of the gradient of the weak solutions. This approach is of independent technical interest, and it is flexible enough to be applied for deriving improved gradient regularity in a larger class of rearrangement-invariant function spaces.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109857"},"PeriodicalIF":2.8,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840626","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 : 2025-12-26DOI: 10.1016/j.aml.2025.109858
João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva
This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index is bounded from below by , where and are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.
{"title":"A lower bound for the Morse index of nodal radial solutions for gradient elliptic systems","authors":"João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva","doi":"10.1016/j.aml.2025.109858","DOIUrl":"10.1016/j.aml.2025.109858","url":null,"abstract":"<div><div>This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is bounded from below by <span><math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>r</mi><mi>a</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109858"},"PeriodicalIF":2.8,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845495","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 : 2025-12-24DOI: 10.1016/j.aml.2025.109856
Dongxiu Wang, Anmin Mao
This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.
{"title":"Global solvability in a mosquito-borne disease system with chemotaxis","authors":"Dongxiu Wang, Anmin Mao","doi":"10.1016/j.aml.2025.109856","DOIUrl":"10.1016/j.aml.2025.109856","url":null,"abstract":"<div><div>This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109856"},"PeriodicalIF":2.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822949","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 : 2025-12-23DOI: 10.1016/j.aml.2025.109855
Huiling Du , Fang Li , Bo Xue
A new nonlinear super vector equation is obtained according to a matrix spectral problem with the help of the compatibility condition. When , the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an -component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with -peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the -component super CH equation are discussed.
{"title":"An n-component super Camassa–Holm equation with N-peakons","authors":"Huiling Du , Fang Li , Bo Xue","doi":"10.1016/j.aml.2025.109855","DOIUrl":"10.1016/j.aml.2025.109855","url":null,"abstract":"<div><div>A new nonlinear super vector equation is obtained according to a <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> matrix spectral problem with the help of the compatibility condition. When <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>, the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an <span><math><mi>n</mi></math></span>-component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with <span><math><mi>N</mi></math></span>-peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the <span><math><mi>n</mi></math></span>-component super CH equation are discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109855"},"PeriodicalIF":2.8,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822954","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 : 2025-12-19DOI: 10.1016/j.aml.2025.109854
Tongtong Sun , Fajie Wang , Xingxing Yue
This paper presents a novel local semi-analytical meshless method, based on the fundamental solutions, for acoustic eigenfrequency and modal analysis in complex two- and three-dimensional domains. The proposed approach requires only a set of discrete nodes distributed within the domain and along its boundary, thereby eliminating the need for mesh generation. By combining the moving least squares approximation with spline weight functions, locally supported coefficient matrices are constructed. The eigenfrequencies and modes are then obtained through the singular value decomposition. This local strategy effectively mitigates numerical instability, addresses the ill-conditioning issues commonly encountered in traditional global meshless methods, and avoids the mesh dependency inherent in the finite element method. Numerical experiments on both two- and three-dimensional cases demonstrate that the proposed method achieves higher computational accuracy compared to the conventional approaches, particularly in capturing high-frequency modal characteristics. The results highlight its potential as an efficient and robust tool for vibration and noise analysis in complex acoustic structures.
{"title":"A novel local semi-analytical meshless method for acoustic eigenfrequency and modal analysis","authors":"Tongtong Sun , Fajie Wang , Xingxing Yue","doi":"10.1016/j.aml.2025.109854","DOIUrl":"10.1016/j.aml.2025.109854","url":null,"abstract":"<div><div>This paper presents a novel local semi-analytical meshless method, based on the fundamental solutions, for acoustic eigenfrequency and modal analysis in complex two- and three-dimensional domains. The proposed approach requires only a set of discrete nodes distributed within the domain and along its boundary, thereby eliminating the need for mesh generation. By combining the moving least squares approximation with spline weight functions, locally supported coefficient matrices are constructed. The eigenfrequencies and modes are then obtained through the singular value decomposition. This local strategy effectively mitigates numerical instability, addresses the ill-conditioning issues commonly encountered in traditional global meshless methods, and avoids the mesh dependency inherent in the finite element method. Numerical experiments on both two- and three-dimensional cases demonstrate that the proposed method achieves higher computational accuracy compared to the conventional approaches, particularly in capturing high-frequency modal characteristics. The results highlight its potential as an efficient and robust tool for vibration and noise analysis in complex acoustic structures.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109854"},"PeriodicalIF":2.8,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784748","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 : 2025-12-18DOI: 10.1016/j.aml.2025.109853
Qiuxiang Tu , Guangjing Song , Changzhou Dong , Qi Liu
Dual quaternions provide a powerful mathematical tool for robust point cloud registration through their compact and unified representation of three-dimensional rigid transformations. In this paper, we present a dual quaternion matrix formulation for 3D point cloud registration via a dual-complex representation. We reformulate the rigid transformation as a complex linear system, which enables the direct and unified computation of rotation and translation without the need for iterative refinement. Numerical experiments are conducted to verify the robustness and effectiveness of the proposed methods.
{"title":"Dual quaternion matrix formulation for robust 3D point cloud registration","authors":"Qiuxiang Tu , Guangjing Song , Changzhou Dong , Qi Liu","doi":"10.1016/j.aml.2025.109853","DOIUrl":"10.1016/j.aml.2025.109853","url":null,"abstract":"<div><div>Dual quaternions provide a powerful mathematical tool for robust point cloud registration through their compact and unified representation of three-dimensional rigid transformations. In this paper, we present a dual quaternion matrix formulation for 3D point cloud registration via a dual-complex representation. We reformulate the rigid transformation as a complex linear system, which enables the direct and unified computation of rotation and translation without the need for iterative refinement. Numerical experiments are conducted to verify the robustness and effectiveness of the proposed methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109853"},"PeriodicalIF":2.8,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786037","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 : 2025-12-15DOI: 10.1016/j.aml.2025.109852
Songhang Yu , Yisi Wang , Jian Zhang
In this paper, we investigate the nonlinear fractional -Laplace problem with potentials and mass constraint. Under some natural assumptions on the potentials, using minimization techniques together with compactness analysis, we establish new existence results of normalized solutions.
{"title":"Normalized solutions for a nonlinear fractional elliptic problem with potentials","authors":"Songhang Yu , Yisi Wang , Jian Zhang","doi":"10.1016/j.aml.2025.109852","DOIUrl":"10.1016/j.aml.2025.109852","url":null,"abstract":"<div><div>In this paper, we investigate the nonlinear fractional <span><math><mi>p</mi></math></span>-Laplace problem with potentials and mass constraint. Under some natural assumptions on the potentials, using minimization techniques together with compactness analysis, we establish new existence results of normalized solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109852"},"PeriodicalIF":2.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753503","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 : 2025-12-13DOI: 10.1016/j.aml.2025.109851
Yana Guo , Ming Li
This paper is devoted to the study of the large time behavior to the two-dimensional MHD-Boussinesq equations with linear velocity damping in . By fully exploiting the special structure of the system and using the uniformly bounded generalized Oseen operator, we establish the decay estimates of the solutions to this system.
{"title":"Decay estimates of 2D Boussinesq equations for MHD convection with stratification effects","authors":"Yana Guo , Ming Li","doi":"10.1016/j.aml.2025.109851","DOIUrl":"10.1016/j.aml.2025.109851","url":null,"abstract":"<div><div>This paper is devoted to the study of the large time behavior to the two-dimensional MHD-Boussinesq equations with linear velocity damping in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. By fully exploiting the special structure of the system and using the uniformly bounded generalized Oseen operator, we establish the decay estimates of the solutions to this system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109851"},"PeriodicalIF":2.8,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731473","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 : 2025-12-13DOI: 10.1016/j.aml.2025.109850
Qiliang Lin, Chenyin Qian
This paper establishes several regularity criteria for the three-dimensional inhomogeneous incompressible Navier–Stokes equations in terms of the horizontal components of the velocity field, allowing for initial densities that contain vacuum. Specifically, we prove that Prodi–Serrin type conditions imposed solely on the horizontal velocity or its gradient in critical spaces ensure regularity of the weak solution, given initial data and .
{"title":"Regularity criteria via horizontal velocity components for 3D inhomogeneous incompressible Navier–Stokes equations with vacuum","authors":"Qiliang Lin, Chenyin Qian","doi":"10.1016/j.aml.2025.109850","DOIUrl":"10.1016/j.aml.2025.109850","url":null,"abstract":"<div><div>This paper establishes several regularity criteria for the three-dimensional inhomogeneous incompressible Navier–Stokes equations in terms of the horizontal components of the velocity field, allowing for initial densities that contain vacuum. Specifically, we prove that Prodi–Serrin type conditions imposed solely on the horizontal velocity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msup></math></span> or its gradient <span><math><mrow><mo>∇</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msup></mrow></math></span> in critical spaces ensure regularity of the weak solution, given initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109850"},"PeriodicalIF":2.8,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731478","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 : 2025-12-12DOI: 10.1016/j.aml.2025.109849
Liqun Qi , Chunfeng Cui , Haibin Chen , Yi Xu
In this paper, we systemically introduce completely positive biquadratic (CPBQ) tensors and copositive biquadratic tensors. We show that all weakly CPBQ tensors are sum of squares tensors, the CPBQ tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPBQ tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses of CPBQ tensors, namely positive biquadratic Cauchy tensors and biquadratic Pascal tensors. We show that a biquadratic Pascal tensor is both strongly CPBQ and positive definite.
{"title":"Completely positive biquadratic tensors","authors":"Liqun Qi , Chunfeng Cui , Haibin Chen , Yi Xu","doi":"10.1016/j.aml.2025.109849","DOIUrl":"10.1016/j.aml.2025.109849","url":null,"abstract":"<div><div>In this paper, we systemically introduce completely positive biquadratic (CPBQ) tensors and copositive biquadratic tensors. We show that all weakly CPBQ tensors are sum of squares tensors, the CPBQ tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPBQ tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses of CPBQ tensors, namely positive biquadratic Cauchy tensors and biquadratic Pascal tensors. We show that a biquadratic Pascal tensor is both strongly CPBQ and positive definite.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109849"},"PeriodicalIF":2.8,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731481","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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