Pub Date : 2026-04-01Epub 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":"2026-04-01","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 : 2026-04-01Epub Date: 2025-12-04DOI: 10.1016/j.aml.2025.109842
Yujia Zhang , Xin Wu , Zhaohai Ma
This study is devoted to proving the exponential stability of traveling wave solutions in a scalar age-structured model with spatial diffusion. By employing a comparison principle coupled with a weighted-energy approach, we demonstrate that traveling wave solutions are exponentially stable. This analytical conclusion is validated through numerical simulations.
{"title":"Exponential stability of traveling waves for a scalar age-structured equation","authors":"Yujia Zhang , Xin Wu , Zhaohai Ma","doi":"10.1016/j.aml.2025.109842","DOIUrl":"10.1016/j.aml.2025.109842","url":null,"abstract":"<div><div>This study is devoted to proving the exponential stability of traveling wave solutions in a scalar age-structured model with spatial diffusion. By employing a comparison principle coupled with a weighted-energy approach, we demonstrate that traveling wave solutions are exponentially stable. This analytical conclusion is validated through numerical simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109842"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689357","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 : 2026-04-01Epub 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":"2026-04-01","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 : 2026-04-01Epub 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":"2026-04-01","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 : 2026-04-01Epub 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":"2026-04-01","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 : 2026-04-01Epub Date: 2025-12-04DOI: 10.1016/j.aml.2025.109841
Henrik Garde
This short note modifies a reconstruction method by the author Garde (2020), for reconstructing piecewise constant conductivities in the Calderón problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map were needed since the piecewise constant partition also was assumed unknown. Here I show how to modify the method in case the partition is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed.
{"title":"Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data","authors":"Henrik Garde","doi":"10.1016/j.aml.2025.109841","DOIUrl":"10.1016/j.aml.2025.109841","url":null,"abstract":"<div><div>This short note modifies a reconstruction method by the author Garde (2020), for reconstructing piecewise constant conductivities in the Calderón problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map were needed since the piecewise constant partition also was assumed unknown. Here I show how to modify the method in case the partition is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109841"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665711","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 : 2026-04-01Epub Date: 2025-11-28DOI: 10.1016/j.aml.2025.109834
Paola Loreti, Daniela Sforza
In this paper, we address the question of estimating the energy decay of integrodifferential evolution equations with glassy memory. This class of memory kernel was not analyzed in previous studies. Moreover, a detailed analysis provides an explicit estimate of the connection between the kernel function’s decay constant and the energy’s decay constant.
{"title":"Energy decay for evolution equations with glassy type memory","authors":"Paola Loreti, Daniela Sforza","doi":"10.1016/j.aml.2025.109834","DOIUrl":"10.1016/j.aml.2025.109834","url":null,"abstract":"<div><div>In this paper, we address the question of estimating the energy decay of integrodifferential evolution equations with glassy memory. This class of memory kernel was not analyzed in previous studies. Moreover, a detailed analysis provides an explicit estimate of the connection between the kernel function’s decay constant and the energy’s decay constant.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109834"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145613965","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 : 2026-03-24DOI: 10.1016/j.aml.2026.109945
Sen Wang, Xian-Feng Zhou, Biao Liu, Xuan-Xuan Xi
{"title":"On L 2 -decay of weak solutions to a class of fractional complex Ginzburg–Landau equations","authors":"Sen Wang, Xian-Feng Zhou, Biao Liu, Xuan-Xuan Xi","doi":"10.1016/j.aml.2026.109945","DOIUrl":"https://doi.org/10.1016/j.aml.2026.109945","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"17 2 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147502129","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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