Mathematical Methods in the Applied Sciences最新文献

{"title":"W\u0000 \u0000 \u0000 m\u0000 ,\u0000 p\u0000 \u0000 \u0000 \u0000 $$ {W}^{m,p} $$\u0000 Compactness of Stationary Kinetic Equation","authors":"Zhen Chao, Jingchun Chen, Cong He, Qian Zhao","doi":"10.1002/mma.70896","DOIUrl":"https://doi.org/10.1002/mma.70896","url":null,"abstract":"<div>\u0000 \u0000 <p>We study stationary kinetic equations and derive compactness results in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {W}^{m,p} $$</annotation>\u0000 </semantics></math> spaces. More precisely, we show that if a solution sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>∈</mo>\u0000 <mi>Λ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {left{{f}_{lambda}left(x,vright)right}}_{lambda in Lambda} $$</annotation>\u0000 </semantics></math> is locally relatively compact in the velocity variable <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation>$$ v $$</annotation>\u0000 </semantics></math>, then it is also locally relatively compact in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(x,vright) $$</annotation>\u0000 </semantics></math>-space, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$$ x $$</annotation>\u0000 </semantics></math> denotes the spatial variable. To prove this result, we established a Fourier-frequency-based characterization of compactness within the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16589-16602"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149029084","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}

{"title":"Existence and Qualitative Properties of Self-Similar Solutions to a Nonlinear Chipot–Weissler Type Equation","authors":"Arij Bouzelmate, Inssaf Raiss","doi":"10.1002/mma.70906","DOIUrl":"https://doi.org/10.1002/mma.70906","url":null,"abstract":"<div>\u0000 \u0000 <p>This article is devoted to the study of radial self-similar solutions of the nonlinear Chipot–Weissler equation \u0000\u0000 </p><div><span><span><!--FIGURE--><span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mi>v</mi>\u0000 <mo>−</mo>\u0000 <mo>|</mo>\u0000 <mo>∇</mo>\u0000 <mi>v</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mo>|</mo>\u0000 <mi>v</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>v</mi>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mtext>in</mtext>\u0000 <mspace></mspace>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16799-16816"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149029189","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}

{"title":"Averaging Principle for Doubly Perturbed McKean–Vlasov SDEs With Common Noise","authors":"Youpeng Wang,&nbsp;Wensheng Yin,&nbsp;Chengcheng Zhong,&nbsp;Yong Ren","doi":"10.1002/mma.70912","DOIUrl":"https://doi.org/10.1002/mma.70912","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we address the issue on averaging principle for doubly perturbed McKean–Vlasov stochastic differential equations (SDEs) with common noise under an averaging condition. Employing the Banach fixed point theorem, we establish the well-posedness of doubly perturbed McKean–Vlasov SDEs with common noise. Under the averaging assumption, we demonstrate that the solutions of the original system converge to those of a simplified time-homogeneous averaged system in the mean-square sense. Finally, an example is provided to show the applications of our results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16790-16798"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027756","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}

{"title":"Carleson Frame Methods for Pantograph-Type Delay Differential Equations: Theory and Applications","authors":"Mutaz Mohammad,&nbsp;Mohyeedden Sweidan,&nbsp;Alexander Trounev","doi":"10.1002/mma.70816","DOIUrl":"https://doi.org/10.1002/mma.70816","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a unified analytic-numerical method for pantograph-type delay differential equations based on Carleson frames. The construction exploits the hyperbolic separation of Carleson sequences in the unit disk together with the diagonal action of contraction-induced composition operators on Hardy spaces. Within this setting, solutions are represented through truncated orbits of a bounded operator, leading to redundant but stable frame expansions that naturally reflect the intrinsic self-similarity of proportional-delay dynamics. We establish well-posedness of the discrete scheme, stability of the expansion coefficients, and quasi-optimal convergence, and we further obtain spectral (geometric) convergence for analytic solutions. For a canonical generator, we derive explicit closed-form expressions for the Gram, delay, and derivative matrices, enabling an efficient and numerically robust implementation. Numerical experiments for both linear and nonlinear pantograph equations confirm the theoretical predictions, demonstrating high accuracy, favorable conditioning, and stable behavior under refinement. To the best of our knowledge, this work provides one of the first systematic numerical frameworks for proportional-delay systems based on Carleson frames, and highlights their potential as a mathematically transparent and effective tool for the analysis and computation of such problems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16545-16566"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027829","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}

{"title":"Riemann–Liouville Type Fractional Derivatives and Equivalences of Linear Riemann–Liouville Type Fractional Differential Equations","authors":"Kunquan Lan","doi":"10.1002/mma.70898","DOIUrl":"https://doi.org/10.1002/mma.70898","url":null,"abstract":"<p>The first or higher order Riemann–Liouville (R-L) type fractional derivatives are studied. The relations between the R-L type fractional derivatives and the classical R-L fractional derivatives are obtained and the spaces of functions on which the R-L type fractional derivatives exist are provided. The identities for the compositions of the R-L type fractional derivatives and the corresponding integral operators are obtained. Some of the above results are new and others generalize some previous known results. A continuity assumption used in the previous equivalence results of linear higher order fractional differential equations (FDEs) in the space of absolutely integrable functions will be dropped. The equivalences of linear higher order FDEs in the space of continuous functions are established and these equivalence results will be useful for further studying boundary value problems of nonlinear FDEs with a variety of boundary conditions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16686-16708"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70898","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust Optimization of High-Dimensional Partially Linear Models Using Huber Loss and Elastic Net","authors":"Jiaxin Fu,&nbsp;Aifen Feng,&nbsp;Minghui Li","doi":"10.1002/mma.70910","DOIUrl":"https://doi.org/10.1002/mma.70910","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes a new Huber-Elastic-Net regression model for partial linear models to address the complex and diverse characteristics of high-dimensional data. It combines the piecewise flexibility of Huber loss function and the mixed penalty term of elastic network to improve the anti-interference ability of outliers and alleviate multicollinearity among high-dimensional variables. Furthermore, we designed the Alternating Direction Method of Multipliers(ADMM) to solve this optimization problem and proved the convergence of this algorithm under certain conditions. Then, we conducted numerical simulations on two types of high-dimensional data, namely multicollinearity and outliers, to demonstrate the mitigating effect and anti-interference ability of the model, and compared and analyzed it with Lasso and Ridge regression methods. Finally, taking Boston housing price data as an example and comparing it with other models, we validated the effectiveness and practicality of the proposed model.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16850-16871"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149028024","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}

{"title":"Convergence of Approximate Solutions for the Transport-Diffusion Equation With Time and Space-Dependent Diffusion Coefficient","authors":"Abdelhamid Bezia,&nbsp;Rabah Gherdaoui","doi":"10.1002/mma.70886","DOIUrl":"https://doi.org/10.1002/mma.70886","url":null,"abstract":"<div>\u0000 <p>In this paper, we study the transport-diffusion equation in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^d $$</annotation>\u0000 </semantics></math> with a diffusion coefficient <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 <mo>=</mo>\u0000 <mi>κ</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ kappa =kappa left(t,xright) $$</annotation>\u0000 </semantics></math> depending on both the position <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ xin {mathbb{R}}^d $$</annotation>\u0000 </semantics></math> and time <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$$ t $$</annotation>\u0000 </semantics></math>. We construct a family of approximate solutions using convolutions with the heat kernel and translations associated with the velocity field over discrete time steps. Under suitable regularity and boundedness assumptions on the given functions, we establish the uniform convergence of these approximate solutions to the solution of the transport-diffusion equation. Furthermore, we prove the uniform convergence of the spatial derivatives of the approximate solutions to the corresponding derivatives of the solution. This method generalizes previous results obtained for constant, space-dependent, and time-dependent diffusion coefficients.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16567-16588"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149029016","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}

{"title":"A Dissipation-Preserving Finite Element Approach for Nonlinear Nonlocal Euler–Bernoulli Equations","authors":"Tao Guo,&nbsp;Kexin Li,&nbsp;Omid Nikan,&nbsp;Xu Xiao","doi":"10.1002/mma.70908","DOIUrl":"https://doi.org/10.1002/mma.70908","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper focuses on the numerical solution of the modified Euler–Bernoulli equation incorporating nonlinear nonlocal viscous damping, which is suitable for modeling vibration phenomena in beams and plates. This formulation is relevant for modeling vibrational phenomena in engineering structures. The proposed strategy produces an approximation of the unknown solution through a two-step numerical process. First, the Galerkin finite element method is used to derive a spatially semi-discrete scheme. Then, a time-stepping difference method is applied to accomplish a fully discrete Galerkin scheme. The energy method is employed to establish the stability and uniqueness of both the semi-discrete and fully discrete solutions. The main difficulty in this work lies in handling the nonlinear viscous damping term during discretization and analysis. Optimal error estimates are obtained for both discretizations. Numerical simulations confirm the theoretical predictions and indicate that the fully discrete scheme efficiently dissipates energy.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 15","pages":"16743-16766"},"PeriodicalIF":2.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027797","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}

{"title":"The Head-Wave Ray Transform","authors":"Maarten V. de Hoop,&nbsp;Antti Kykkänen,&nbsp;Rohit Kumar Mishra","doi":"10.1002/mma.70846","DOIUrl":"https://doi.org/10.1002/mma.70846","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce and study a new integral ray transform called the head-wave transform. The head-wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths corresponds to ray paths of head-waves propagating in a medium with sharp changes in sound speed. The middle part of the ray paths corresponds to gliding along the so-called gliding surface. As our main results, we prove inversion formulas and null space characterizations under multiple different sets of assumptions on the geometry of the gliding surface and the integrand function.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15628-15646"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753481","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}

{"title":"Averaging Principle for A Stochastic Delayed Avian Influenza Model with Impulsive Perturbations and Fractional Riemann-Liouville-Type Contact Rates","authors":"ShuangYan Yang,&nbsp;Kui Liu","doi":"10.1002/mma.70841","DOIUrl":"https://doi.org/10.1002/mma.70841","url":null,"abstract":"<div>\u0000 \u0000 <p>Upon exposure to infectious individuals, susceptible hosts exhibit heterogeneous clinical manifestations ranging from viral carriage without overt symptomatology to progressive symptomatic infection under the effects of the incubation period and external environmental disturbances. Meanwhile, the current rate of change in the number of susceptible hosts is influenced not only by ongoing contact with infected hosts during the incubation period, but also by previous interactions. To characterize the memory and historical cumulative effects of this infection process, this paper formulates a stochastic delayed avian influenza model with impulsive perturbations and fractional Riemann-Liouville-type contact rates. The well-posedness of mild solutions for this model is established using the semigroup method and the Banach fixed-point theorem. Additionally, an averaging principle is derived by employing inequality techniques and appropriate transformations for the fractional avian influenza model. The theoretical results indicate that the solution of the original impulsive avian influenza system can be effectively approximated by that of a simplified non-impulsive temporally averaged stochastic system, thereby providing a way to reduce system complexity. Numerical simulations are presented to validate the theoretical results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15647-15673"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753466","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}