Mathematical Methods in the Applied Sciences最新文献

{"title":"Energy Decay Estimates for the Wave Equation With Logarithmic Feedback","authors":"Donghao Li,&nbsp;Chenxia Zhang,&nbsp;Hongwei Zhang","doi":"10.1002/mma.10871","DOIUrl":"https://doi.org/10.1002/mma.10871","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, a semilinear wave equation with logarithmic feedback is considered. The polynomial decay of the energy is obtained. The method of proof is based on multipliers technique, on a integral inequality, and on some special algebraic inequalities. The results complement those of the literature about logarithmic damping, and it seem to be an interesting problem in the unknown land of weak damping mechanics.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10110-10113"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949718","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":"Construction of Normal-Regular Solutions of Inhomogeneous System of Partial Differential Equations of Second Order","authors":"Meiramgul Talipova","doi":"10.1002/mma.10828","DOIUrl":"https://doi.org/10.1002/mma.10828","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider an inhomogeneous system of second-order partial differential equations with regular singularities at the point (0, 0). The Frobenius-Latysheva method is used to find normally regular solutions. A universal approach to constructing solutions in the vicinity of regular singularities has been developed, the number of linearly independent partial solutions has been determined, and compatibility and integrability conditions have been investigated. Concrete examples demonstrate the use of the method of uncertain coefficients to obtain partial solutions of inhomogeneous systems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9618-9623"},"PeriodicalIF":2.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950335","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":"Weighted Estimates of the Weyl-Type Operator and Its Compactness","authors":"Akbota Abylayeva,&nbsp;Alisher Otegen","doi":"10.1002/mma.10834","DOIUrl":"https://doi.org/10.1002/mma.10834","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, the results of the necessity and sufficiency conditions of the fact that the operator \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ T $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for the case \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ boldsymbol{p}boldsymbol{le}boldsymbol{q} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is bounded and compact from the weighted Lebesgue space \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&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;mi&gt;w&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&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;mi&gt;w&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {L}_{p,w}&amp;#x0003D;{L}_{p,w}(I) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to weighted Lebesgue space \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {L}_{q,v}&amp;#x0003D;{L}_{q,v}(I) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are obtained, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&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;mi&gt;w&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9676-9683"},"PeriodicalIF":2.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950336","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":"Global Existence and Blow-Up Phenomenon of Solution for a Viscoelastic Wave Equation With Nonlinear Degenerate Damping and Logarithmic Source Term","authors":"Shubin Wang,&nbsp;Zijian Du","doi":"10.1002/mma.10842","DOIUrl":"https://doi.org/10.1002/mma.10842","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper deals with the initial boundary value problem for degenerate damped nonlinear wave equations with logarithmic nonlinearity, given by the equation: \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;g&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;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&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;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&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;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&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;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mi&gt;ln&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9778-9795"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950569","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":"Dynamic Behaviors of the Dark Higher Order Rogue Waves and Interaction Inductions of a (3 + 1)-Dimensional Model","authors":"Na Cao,&nbsp;XiaoJun Yin,&nbsp;LiYang Xu,&nbsp;ChunXia Wang","doi":"10.1002/mma.10836","DOIUrl":"https://doi.org/10.1002/mma.10836","url":null,"abstract":"<div>\u0000 \u0000 <p>The research obtained dark second-order rogue waves and two sets of interaction solutions for (3 + 1)-dimensional equation by using symbolic calculation and two induction formulas. The two sets of interaction solutions are about second-order rogue waves and multiple stripes, second-order rogue waves and multiple solitons. Six sets of composite diagrams are made to show the interactions in three dimensions. The second-order rogue waves merge from two low-amplitude tops into one high-amplitude top if they meet with multiple stripes, and the amplitude increases with the increase of stripes' number. The second-order rogue waves are usually generated in the center of two kinky solitons if they meet with multiple solitons, and the amplitude increases with the increase of solitons' number. No matter what kind of rendezvous, we see the energy transfer from solitons to rogue waves and back to solitons. This will be useful in studying the evolution of rogue wave.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9695-9706"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950570","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":"Spin 1 Particle With Anomalous Magnetic Moment in External Uniform Electric Field, Solutions With Cylindrical Symmetry","authors":"Alina Ivashkevich,&nbsp;Viktor Red'kov,&nbsp;Alexander Chichurin","doi":"10.1002/mma.10831","DOIUrl":"https://doi.org/10.1002/mma.10831","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;A generalized 10-dimensional Duffin–Kemmer–Petiau equation for spin 1 particle with anomalous magnetic moment is examined in cylindrical coordinates \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&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;r&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(t,r,phi, zright) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the presence of the external uniform electric field oriented along the axis \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ z $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. On solutions, we diagonalize operators of the energy and third projection of the total angular momentum. First, we derive the system of 10 equations in partial derivatives for functions \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&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;mi&gt;z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&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;msub&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;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;10&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;‾&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {F}_ileft(r,zright)&amp;#x0003D;{G}_i(r){H}_i(z)kern0.3em left(i&amp;#x0003D;overline{1,10}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The use of the method based on the projective operators permits us to express 10 variables \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9640-9652"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950568","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":"Multiple Solutions for a Variable-Order p(x,·)-Kirchhoff-Type Problem With Weight","authors":"E. Azroul,&nbsp;N. Kamali,&nbsp;M. Shimi","doi":"10.1002/mma.10808","DOIUrl":"https://doi.org/10.1002/mma.10808","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we establish the existence of three weak solutions for a Kirchhoff-type problem with weight that involves the variable-order \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mo>·</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ pleft(x,cdotp right) $$</annotation>\u0000 </semantics></math>-Laplacian operator. We introduce a suitable functional framework for addressing such problems and establish a fundamental continuous and compact embedding theorem of this framework. Using Ricceri's three critical point approach, we prove the existence of weak solutions in the context of weighted variable-order Sobolev spaces with variable exponents.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9430-9439"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950566","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":"Global Classical Solutions for a Chemotaxis System of Attraction–Repulsion With Singular Sensitivity","authors":"S. Amalorpava Josephine,&nbsp;S. Karthikeyan,&nbsp;L. Shangerganesh,&nbsp;K. Yadhavan","doi":"10.1002/mma.10806","DOIUrl":"https://doi.org/10.1002/mma.10806","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper examines the singular sensitive parabolic attraction–repulsion chemotaxis system with two chemicals subjected to the Neumann boundary condition. Two chemical substances impact the species involved in this biological process. Both signals come from the same species, but a higher concentration of one attracts the species while a lesser concentration repels it. Using the energy estimate approach, we explore the global existence of classical solutions of the proposed model in a spatial domain with a dimension greater than one.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9404-9413"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950529","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":"Pullback Attractors for Nonautonomous Reaction–Diffusion Equations With the Driving Delay Term in ℝN","authors":"Yong Ren,&nbsp;Yongqin Xie,&nbsp;Jiangwei Zhang","doi":"10.1002/mma.10843","DOIUrl":"https://doi.org/10.1002/mma.10843","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we mainly investigate the asymptotic behavior of nonautonomous reaction–diffusion equation with the driving delay term in whole space. A new method (or technique) is introduced for verifying the \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left({C}_{L&amp;amp;amp;#x0005E;2left({mathbb{R}}&amp;amp;amp;#x0005E;Nright)},{C}_{H&amp;amp;amp;#x0005E;1left({mathbb{R}}&amp;amp;amp;#x0005E;Nright)}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-pullback \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝒟&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;-asymptotic compactness of the family of processes (see Theorem 2). As an application, the \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9796-9808"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949874","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":"Modeling Immobilized Enzyme Reactions: Nonlinear Kinetics With Fractional- and Integer-Order Analysis","authors":"R. Rajaraman","doi":"10.1002/mma.10791","DOIUrl":"https://doi.org/10.1002/mma.10791","url":null,"abstract":"<div>\u0000 \u0000 <p>This research investigates the immobilization of enzymes within porous materials of varying geometries, such as spherical and cylindrical pellet-shaped catalysts. The study focuses on modeling enzyme reactions using reaction–diffusion equations that capture the irreversible Michaelis–Menten kinetics, emphasizing the nonlinear nature of the process. A distinctive feature of this work is the incorporation of fractional derivatives to enhance the understanding of enzymatic reaction kinetics. To achieve this, a novel computational framework utilizing Laguerre wavelets is developed to compute substrate concentrations and effectiveness factors over a broad range of parameter values. The proposed Laguerre wavelet method (LAWM) is rigorously compared against established analytical and numerical approaches, including the Hermite wavelet method (HWM), Taylor series method (TSM), Adomian decomposition method (ADM), and the fourth-order Runge–Kutta method (RKM). The findings reveal a high degree of accuracy and consistency across all methods, underscoring the reliability and efficiency of the LAWM. This study offers new insights into enzyme kinetics within porous catalysts and highlights the potential of fractional-order models for advancing biocatalytic applications. The outcomes provide a robust theoretical foundation for optimizing the design and performance of immobilized enzyme reactors in industrial and biotechnological settings.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9177-9193"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909601","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}