Mathematical Methods in the Applied Sciences最新文献

{"title":"Observer-Based Boundary Control for Coupled Parabolic PDEs With Spatially Varying Coefficients","authors":"Seyedamin Hatami,&nbsp;Mohammad Keyanpour","doi":"10.1002/mma.70943","DOIUrl":"https://doi.org/10.1002/mma.70943","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper addresses the observer-based output-feedback boundary control design for a system of <span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-coupled parabolic partial differential equations (PDEs) with spatially varying diffusion coefficients without any ordering conditions. First, a boundary observer is proposed to estimate the system states, with its gain determined by considering a stable target system and using a backstepping transformation method. To design an observer-based boundary controller for <span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-coupled parabolic PDE systems, we construct a backstepping transformation that maps the observer dynamics into a stable target system, yielding the associated kernel and boundary control law, which is the main contribution of this work. Furthermore, analytical solutions to two sets of kernel equations are derived to determine the controller and observer gains. By employing Lyapunov stability analysis, we prove that the proposed output-feedback architecture guarantees exponential stability of the entire closed-loop system. Finally, numerical simulations are conducted to validate the theoretical results of the proposed method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17933-17951"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311603","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":"Space-Time Spectral Element Method for PIDEs Arising in Finance","authors":"Zhiyuan Hui,&nbsp;Xuchen Jin,&nbsp;Changtao Sheng","doi":"10.1002/mma.70948","DOIUrl":"https://doi.org/10.1002/mma.70948","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes an efficient space-time spectral element method for option pricing under the Merton jump-diffusion model. The model gives rise to a partial integro-differential equation (PIDE) with a nonlocal integral term and temporal singularities due to nonsmooth initial data. To resolve these singularities and ensure high-order accuracy, we employ an <span></span><math>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mi>p</mi>\u0000 </mrow></math>-version of continuous Galerkin scheme with graded time steps. For the spatial discretization, we employ a Laguerre–Legendre composite spectral element method on unbounded domains, which attains spectral accuracy with relatively few degrees of freedom for solutions with slope discontinuities. The resulting space-time discretization gives rise to highly ill-conditioned and nonsymmetric linear systems. To address this difficulty, we design a stable and efficient solver based on QZ decomposition and demonstrate its superiority over tensor-product direct solvers and eigenvalue decomposition methods. Numerical experiments confirm the predicted spectral convergence and highlight the accuracy and efficiency of the proposed method in comparison with existing approaches.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17739-17762"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312360","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":"High-Order Singularity-Corrected Sum-of-Exponentials Product Integration for Second-Kind Fractional Volterra Equations With Modulated Weakly Singular Kernels","authors":"Zahra Masouri,&nbsp;Saeed Hatamzadeh,&nbsp;Tofigh Allahviranloo","doi":"10.1002/mma.70970","DOIUrl":"https://doi.org/10.1002/mma.70970","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Weakly singular fractional Volterra equations require both accurate treatment of the algebraic kernel singularity and efficient evaluation of the growing history term. We develop a singularity-corrected sum-of-exponentials product-integration framework for second-kind equations with kernels &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;. Product integration treats the local singularity analytically, while sum-of-exponentials (SOE) compression converts the resolved Abel-type history into causal recurrences. For smooth data, the degree-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; method satisfies an error bound of order &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;soe&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;; a reduced-regularity estimate is also established for algebraically singular solutions. Smooth non-convolution modulations are handled by diagonal splitting, and a separated rank-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; approximation yields a fully accelerated variant with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; work and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17999-18039"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311855","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":"On the Global Asymptotic Stability of an Infection-Age-Structured Competitive Model","authors":"S. Girel,&nbsp;Q. Richard","doi":"10.1002/mma.70967","DOIUrl":"https://doi.org/10.1002/mma.70967","url":null,"abstract":"<p>We investigate an infection-age-structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a complete characterization of the asymptotic behavior for an arbitrary number of populations without assuming uniqueness of the maximal reproduction number. By means of integrated semigroups theory, persistence results, and Lyapunov functionals, we establish global asymptotic stability of equilibria and extend previous results obtained for simpler (ODE) models. A key contribution lies in overcoming technical difficulties related to the definition and differentiation of Lyapunov functionals, as well as in refining arguments based on the LaSalle invariance principle.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"18040-18072"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70967","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311939","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":"New Hermite–Hadamard Type Bounds for Co-ordinated Convex Functions via Non-Conformable Fractional Integrals","authors":"Arslan Razzaq,&nbsp;Zhouchao Wei","doi":"10.1002/mma.70968","DOIUrl":"https://doi.org/10.1002/mma.70968","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we establish two new identities for functions of two variables and use them to provide new Hermite–Hadamard (H-H)-type fractional integral inequalities for double non-conformable fractional integrals operators whose derivatives are bounded or co-ordinate convex functions on <span></span><math>\u0000 <mrow>\u0000 <mi>Θ</mi>\u0000 <mo>:</mo>\u0000 <mo>=</mo>\u0000 <mo>[</mo>\u0000 <mi>ζ</mi>\u0000 <mo>,</mo>\u0000 <mi>η</mi>\u0000 <mo>]</mo>\u0000 <mo>×</mo>\u0000 <mo>[</mo>\u0000 <mi>ς</mi>\u0000 <mo>,</mo>\u0000 <mi>ϑ</mi>\u0000 <mo>]</mo>\u0000 </mrow></math> in <span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> with <span></span><math>\u0000 <mrow>\u0000 <mi>ζ</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>η</mi>\u0000 </mrow></math> and <span></span><math>\u0000 <mrow>\u0000 <mi>ς</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>ϑ</mi>\u0000 </mrow></math>.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17983-17998"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311741","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":"Leighton–Wintner-Type Oscillation Criteria for the \u0000 \u0000 p\u0000 (\u0000 t\u0000 )\u0000 -Laplacian Dynamic Equations on Time Scales","authors":"Kōdai Fujimoto,&nbsp;Kazuki Ishibashi,&nbsp;Masakazu Onitsuka","doi":"10.1002/mma.70941","DOIUrl":"https://doi.org/10.1002/mma.70941","url":null,"abstract":"<p>This study investigates oscillation problems for <span></span><math>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>-Laplacian dynamic equations on time scales. By employing the Riccati transformation technique, we establish a new Leighton–Wintner-type oscillation theorem for the equations under consideration, which unifies and extends existing results for both differential and difference equations. As illustrative examples, we present several equations, including differential equations on <span></span><math>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow></math>, difference equations on <span></span><math>\u0000 <mrow>\u0000 <mi>ℕ</mi>\u0000 </mrow></math>, equations on hybrid time scales combining continuous and discrete parts, and <span></span><math>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow></math>-difference equations, and show that all proper solutions are oscillatory. The effectiveness of the obtained results is confirmed through numerical simulations.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17617-17626"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70941","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312021","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":"Identification of the Time-Dependent Coefficients in the Fractional Diffusion Equation With Two-Point Boundary Conditions","authors":"Bauyrzhan Derbissaly,&nbsp;Arshyn Altybay,&nbsp;Daurenbek Serikbaev","doi":"10.1002/mma.70958","DOIUrl":"https://doi.org/10.1002/mma.70958","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we investigate an inverse problem of identifying a time-dependent coefficient in a time-fractional diffusion equation with two-point boundary conditions. The unknown coefficient is recovered from an overdetermination condition prescribed at the midpoint of the spatial interval. Since the corresponding boundary conditions are not strongly regular, the direct Fourier method cannot be applied to the original spectral problem. We overcome this difficulty by decomposing the solution into symmetric and antisymmetric parts and reducing the original problem to two auxiliary problems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17888-17917"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311604","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":"Zika Endemicity Lowers the HIV Invasion Threshold: A Mathematical Model of Zika-HIV Coinfection","authors":"Debnarayan Khatua,&nbsp;Bapin Mondal,&nbsp;Md Sadikur Rahman,&nbsp;Sishu Shankar Muni","doi":"10.1002/mma.70945","DOIUrl":"https://doi.org/10.1002/mma.70945","url":null,"abstract":"<div>\u0000 \u0000 <p>The coexistence of Zika virus (ZIKV) and HIV across tropical areas presents important research opportunities to examine how vector-borne pathogens affect trends of sexually transmitted diseases. We create a detailed mathematical model that combines vector-borne transmission with sexual transmission, antiretroviral treatment, coinfection disease development, human movement across multiple population systems, and seasonal changes in mosquito populations, which are forced by climate. The research presents a new concept that defines an effective coinfection invasion reproduction number that describes how HIV establishes itself in populations where the Zika virus circulates. Analytical results demonstrate that endemic Zika transmission decreases the HIV invasion threshold, which allows HIV to survive even when the classical HIV reproduction number falls below one. The analysis of the center manifold and bifurcation demonstrates that the threshold reduction happens through forward transcritical bifurcations. The coinfection persistence patterns reveal three main factors: mosquito biting intensity, HIV transmission rate, and ART-related parameters, while spatial connectivity and climate variability increase the epidemic burden. The study shows that co-endemic areas need climate-aware treatments based on human mobility patterns to create successful intervention strategies.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17763-17792"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312262","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":"Computational Analysis of Modified Baskakov Durrmeyer Operators: Local and Weighted Approximation","authors":"Razi Ahmad,&nbsp;Ayaz Ahmad,&nbsp;Nadeem Rao","doi":"10.1002/mma.70946","DOIUrl":"https://doi.org/10.1002/mma.70946","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we present a Durrmeyer variant of the recently proposed Baskakov–Schurer–Stancu operators. The new operators use a Beta-type integral kernel, which extends approximation capabilities for Lebesgue measurable functions. We start by establishing basic estimates and central moments, providing detailed proofs. Next, we use a weighted modulus of continuity to derive three theorems about the rate of convergence. Then, we prove three weighted approximation theorems through Korovkin-type results in weighted spaces. Additionally, we establish a Voronovskaja-type theorem with an asymptotic error estimate. The results show that the new operators maintain the flexibility of parameters <span></span><math>\u0000 <mrow>\u0000 <mi>ϑ</mi>\u0000 <mo>,</mo>\u0000 <mi>ψ</mi>\u0000 <mo>,</mo>\u0000 <mi>ρ</mi>\u0000 </mrow></math> while offering better smoothness and convergence rates. Finally, we include graphical examples to demonstrate the effectiveness, accuracy, and approximation behavior of the proposed operators.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17727-17738"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312359","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":"Exact Boundary Controllability for Wave Equations With Space Variable Potential","authors":"Ruikson. S. O. Nunes,&nbsp;Miguel R. Nuñez-Chávez,&nbsp;Marcelo Moreira Cavalcanti","doi":"10.1002/mma.70935","DOIUrl":"https://doi.org/10.1002/mma.70935","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this article, we study an exact boundary controllability problem for a wave equation with a potential that varies in the space on non-smooth domains of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 \u0000 &lt;semantics&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;msup&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;annotation&gt;\u0000$$ {mathbb{R}}^n $$\u0000&lt;/annotation&gt;\u0000 &lt;/semantics&gt;\u0000 &lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 \u0000 &lt;semantics&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;annotation&gt;\u0000$$ nge 3 $$\u0000&lt;/annotation&gt;\u0000 &lt;/semantics&gt;\u0000 &lt;/math&gt;. The potential &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 \u0000 &lt;semantics&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;annotation&gt;\u0000$$ p $$\u0000&lt;/annotation&gt;\u0000 &lt;/semantics&gt;\u0000 &lt;/math&gt; considered is a positive space variable function which has the short-range property, that is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 \u0000 &lt;semantics&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;annotation&gt;\u0000$$ p(x)to 0 $$\u0000&lt;/annotation&gt;\u0000 &lt;/semantics&gt;\u0000 &lt;/math&gt; when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 \u0000 &lt;semantics&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;annotation&gt;\u0000$$ mid xmid to +infty $$\u0000&lt;/annotation&gt;\u0000 &lt;/semantics&gt;\u0000 &lt;/math&gt;. The obtained control function is of Neumann type, square integrable and acts on all boundary of the considered domain. The result is obtained using the controllability method established by David L. Russell, taking advantage of the local energy decay estimates for the problem established by Vodev, combined with trace theorems due to Daniel Tataru.&lt;/p&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 16","pages":"17420-17429"},"PeriodicalIF":2.0,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099981","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}