Journal of Mathematical Analysis and Applications最新文献

{"title":"Self-similar solutions of fast-reaction limit problems with nonlinear diffusion","authors":"Elaine Crooks,&nbsp;Yini Du","doi":"10.1016/j.jmaa.2025.129636","DOIUrl":"10.1016/j.jmaa.2025.129636","url":null,"abstract":"<div><div>In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span>, spatial segregation results in the two components of the original systems converging to the positive and negative parts of a self-similar limit profile <span><math><mi>f</mi><mo>(</mo><mi>η</mi><mo>)</mo></math></span>, where <span><math><mi>η</mi><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt></mrow></mfrac></math></span>, that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span> limit problems is proved by using shooting methods which focus on <em>a</em>, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and <em>γ</em>, the derivative of <span><math><mo>−</mo><mi>ϕ</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></span> at <span><math><mi>η</mi><mo>=</mo><mi>a</mi></math></span>. The position of the free boundary gives us intuition about how one substance penetrates into the other, and for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129636"},"PeriodicalIF":1.2,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090559","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":"Minimality criteria for rational functions over Zp","authors":"Sangtae Jeong,&nbsp;Yongjae Kwon","doi":"10.1016/j.jmaa.2025.129624","DOIUrl":"10.1016/j.jmaa.2025.129624","url":null,"abstract":"<div><div>In this paper, we characterize the minimality criteria for a rational function on <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> where the denominator possesses no zeros modulo <em>p</em>. This characterization is specifically formulated regarding the coefficients of a rational function, focusing on cases where <em>p</em> equals 2 or 3. For an arbitrary prime <span><math><mi>p</mi><mo>≥</mo><mn>5</mn></math></span>, we provide an explicit formulation of the minimality criterion for such functions, contingent on the successful determination of the prescribed minimal conditions for the reduction of <em>f</em> modulo <em>p</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129624"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908202","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 invariance of holomorphic mappings of the Hartogs domain over the minimal ball","authors":"Enchao Bi ,&nbsp;Huan Yang ,&nbsp;Qiannan Zhang","doi":"10.1016/j.jmaa.2025.129623","DOIUrl":"10.1016/j.jmaa.2025.129623","url":null,"abstract":"<div><div>In this paper, we study a family of generalized Hartogs type domain over the minimal ball, which is defined by the inequality <span><math><msup><mrow><mo>‖</mo><mi>z</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>|</mo><mi>z</mi><mo>⋅</mo><mi>z</mi><mo>|</mo><mo>&lt;</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mo>‖</mo><mi>w</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span>, where <span><math><mo>(</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>. We will show that the collection of all the holomorphic self-mappings of the Hartogs type domain over a minimal ball keeping the slice function invariant form a subgroup of the automorphism group. As an application, we can build a rigidity result for the automorphism group of the generalized Hartogs type domain over the minimal ball with <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129623"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918335","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 a critical superlinear fractional (p,q)-Kirchhoff equation","authors":"Teresa Isernia","doi":"10.1016/j.jmaa.2025.129626","DOIUrl":"10.1016/j.jmaa.2025.129626","url":null,"abstract":"<div><div>We study ground state solutions to the following fractional <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-Kirchhoff equation<span><span><span><math><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mi>u</mi><mo>+</mo><mrow><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>s</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mrow><mo>(</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mo>=</mo><mi>λ</mi><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>+</mo><mi>Q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><msubsup><mrow><mi>q</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mspace></mspace><mtext> in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn></math></span> are constants, <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> is a parameter sufficiently large, <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>q</mi></math></span> and <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>&lt;</mo><mi>s</mi><mi>q</mi><mo>&lt;</mo><mn>3</mn></math></span>. Here <em>V</em> is a periodic potential, the weight functions <span><math><mi>K</mi></math></span> and <span><math><mi>Q</mi></math></span> are positive and continuous functions, and <em>f</em> is a subcritical nonlinearity that does not satisfy the Ambrosetti–Rabinowitz condition. By using appropriate variational argument, we prove the existence of ground state solutions for <em>λ</em> large.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129626"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918333","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":"Hausdorff measure and decay rate of Riesz capacity","authors":"Qiuling Fan,&nbsp;Richard S. Laugesen","doi":"10.1016/j.jmaa.2025.129625","DOIUrl":"10.1016/j.jmaa.2025.129625","url":null,"abstract":"<div><div>The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129625"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918334","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 fundamental gap of a kind of two dimensional sub-elliptic operator","authors":"Hongli Sun ,&nbsp;Donghui Yang ,&nbsp;Xu Zhang","doi":"10.1016/j.jmaa.2025.129619","DOIUrl":"10.1016/j.jmaa.2025.129619","url":null,"abstract":"<div><div>This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> when <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is subject to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm constraint.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129619"},"PeriodicalIF":1.2,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918277","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 note on weighted sums of i.i.d. random variables","authors":"João Lita da Silva","doi":"10.1016/j.jmaa.2025.129618","DOIUrl":"10.1016/j.jmaa.2025.129618","url":null,"abstract":"<div><div>Given a sequence <span><math><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>n</mi><mo>⩾</mo><mn>1</mn><mo>}</mo></math></span> of independent and identically distributed random variables such that <span><math><mi>E</mi><mo>|</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>&lt;</mo><mo>∞</mo></math></span> for some <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>2</mn></math></span>, and a triangular array <span><math><mo>{</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>,</mo><mn>1</mn><mo>⩽</mo><mi>j</mi><mo>⩽</mo><mi>n</mi><mo>,</mo><mi>n</mi><mo>⩾</mo><mn>1</mn><mo>}</mo></math></span> of real numbers monotonic with respect to one of the indices satisfying <span><math><msub><mrow><mi>max</mi></mrow><mrow><mn>1</mn><mo>⩽</mo><mi>j</mi><mo>⩽</mo><mi>n</mi></mrow></msub><mo>⁡</mo><mo>|</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>|</mo><mo>=</mo><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span>, it is shown that <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>−</mo><mi>E</mi><mspace></mspace><msub><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mover><mo>⟶</mo><mtext>a.s.</mtext></mover><mn>0</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129618"},"PeriodicalIF":1.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913047","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 boundedness in a chemotaxis-Stokes system with nonlinear diffusion mechanism involving gradient dependent flux limitation and indirect signal production","authors":"Yuxin Yan,&nbsp;Zhongping Li","doi":"10.1016/j.jmaa.2025.129621","DOIUrl":"10.1016/j.jmaa.2025.129621","url":null,"abstract":"<div><div>This paper is concerned with the Keller-Segel-Stokes system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>n</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>n</mi><mo>=</mo><mi>Δ</mi><msup><mrow><mi>n</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>−</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>n</mi><mi>f</mi><mo>(</mo><mo>|</mo><mi>∇</mi><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mi>∇</mi><mi>v</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>v</mi><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><mi>w</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>w</mi><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>n</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>∇</mi><mi>P</mi><mo>+</mo><mi>n</mi><mi>∇</mi><mi>ϕ</mi><mo>,</mo><mspace></mspace><mi>∇</mi><mo>⋅</mo><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> under no-flux/no-flux/no-flux/Dirichlet boundary conditions in a smoothly bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, with given suitably regular functions <em>f</em> and <em>ϕ</em>, as well as <em>f</em> satisfies <span><math><mi>f</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>⩽</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>f</mi></mrow></msub><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow><mrow><mo>−</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span>, <span><math><mi>ξ</mi><mo>⩾</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span>. It is shown that for all suitably regular initial data the associated initial-boundary value problem possesses at least one globally bounded weak solution provided <span><math><mn>9</mn><mi>m</mi><mo>+</mo><mn>4</mn><mi>α</mi><mo>&gt;</mo><mn>10</mn></math></span>. Our result strictly proved that the volume saturation effect is indeed conductive to the global existence and boundedness of the three-dimensional Keller-Segel-Stokes system.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129621"},"PeriodicalIF":1.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878920","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":"Chaos expansion solutions of a class of magnetic Schrödinger Wick-type stochastic equations on Rd","authors":"Sandro Coriasco ,&nbsp;Stevan Pilipović ,&nbsp;Dora Seleši","doi":"10.1016/j.jmaa.2025.129620","DOIUrl":"10.1016/j.jmaa.2025.129620","url":null,"abstract":"<div><div>We treat some classes of linear and semilinear stochastic partial differential equations of Schrödinger type on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, involving a non-flat Laplacian, within the framework of white noise analysis, combined with Wiener-Itô chaos expansions and pseudodifferential operator methods. The initial data and potential term of the Schrödinger operator are assumed to be generalized stochastic processes that have spatial dependence. We prove that the equations under consideration have unique solutions in the appropriate (intersections of weighted) Sobolev-Kato-Kondratiev spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129620"},"PeriodicalIF":1.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903601","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 numerical study of a continuous Petrov-Galerkin method for the nonlinear convection-diffusion equation","authors":"Zhihui Zhao,&nbsp;Hong Li,&nbsp;Wei Gao","doi":"10.1016/j.jmaa.2025.129617","DOIUrl":"10.1016/j.jmaa.2025.129617","url":null,"abstract":"<div><div>This paper aims to use the continuous Petrov-Galerkin (CPG) method to study the nonlinear convection-diffusion equation. This method discretizes the time and space variables simultaneously with the finite element (FE) method, thus it is convenient to derive high order accuracy in time and space and has better numerical stability. In addition, the Petrov-Galerkin method is employed to approximate the model problem, which can reduce the computational scale in comparison with the usual Galerkin method. We demonstrate the existence and uniqueness of the CPG solution and give the convergence analysis without the constraints of spatial grid parameter. Several numerical tests are performed to access the validity and the numerical stability of the CPG method. Also, numerical tests illustrate that the CPG method is superior to the standard finite element (SFE) method and the continuous Galerkin (CG) method in solving the nonlinear convection-diffusion equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129617"},"PeriodicalIF":1.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878747","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}