Pub Date : 2026-09-15Epub Date: 2026-03-04DOI: 10.1016/j.jmaa.2026.130577
Jeongmin Han
In this paper, we investigate a class of tug-of-war games that incorporate a constant payoff discount rate at each turn. The associated model problems are p-Laplace type partial differential equations with zeroth-order terms. We establish existence, uniqueness, and regularity results for the corresponding game value functions. Furthermore, we explore properties of the solutions to the model PDEs, informed by the analysis of the underlying games.
{"title":"Tug-of-war games related to p-Laplace type equations with zeroth order terms","authors":"Jeongmin Han","doi":"10.1016/j.jmaa.2026.130577","DOIUrl":"10.1016/j.jmaa.2026.130577","url":null,"abstract":"<div><div>In this paper, we investigate a class of tug-of-war games that incorporate a constant payoff discount rate at each turn. The associated model problems are <em>p</em>-Laplace type partial differential equations with zeroth-order terms. We establish existence, uniqueness, and regularity results for the corresponding game value functions. Furthermore, we explore properties of the solutions to the model PDEs, informed by the analysis of the underlying games.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"561 2","pages":"Article 130577"},"PeriodicalIF":1.2,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147388327","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}
Pub Date : 2026-08-15Epub Date: 2026-02-09DOI: 10.1016/j.jmaa.2026.130489
Luan Hoang , Akif Ibragimov
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition. Starting with the reduced linear problem, we obtain the asymptotic estimates for the solutions, as time , depending on the asymptotic behavior of the forcing term and boundary data. These are established in both cases when the drifts are uniformly bounded, and unbounded as . For the nonlinear problem, we prove the convergence of the solutions under suitable conditions that balance the growth of the nonlinear term with the decay of the data. To take advantage of the diffusion in the non-divergence form, we prove an inhomogeneous version of the Landis-typed Growth Lemma and apply it to successive time-intervals. At each time step, the center for the barrier function is selected carefully to optimize the contracting factor. Our rigorous results show the robustness of the model.
{"title":"Asymptotic estimates for solutions of inhomogeneous non-divergence diffusion equations with drifts","authors":"Luan Hoang , Akif Ibragimov","doi":"10.1016/j.jmaa.2026.130489","DOIUrl":"10.1016/j.jmaa.2026.130489","url":null,"abstract":"<div><div>We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition. Starting with the reduced linear problem, we obtain the asymptotic estimates for the solutions, as time <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>, depending on the asymptotic behavior of the forcing term and boundary data. These are established in both cases when the drifts are uniformly bounded, and unbounded as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>. For the nonlinear problem, we prove the convergence of the solutions under suitable conditions that balance the growth of the nonlinear term with the decay of the data. To take advantage of the diffusion in the non-divergence form, we prove an inhomogeneous version of the Landis-typed Growth Lemma and apply it to successive time-intervals. At each time step, the center for the barrier function is selected carefully to optimize the contracting factor. Our rigorous results show the robustness of the model.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 2","pages":"Article 130489"},"PeriodicalIF":1.2,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154233","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}
Pub Date : 2026-08-15Epub Date: 2026-02-10DOI: 10.1016/j.jmaa.2026.130499
Sandeep Kumar Verma, Athulya P
In this work, we introduce the β-semigroup for , which unifies and extends the classical Poisson (for ) and heat (for ) semigroups within the Dunkl analysis framework. Leveraging this semigroup, we derive an explicit representation for the inverse of the Dunkl–Riesz potential and characterize the image of the function space for . We further define the bi-parametric potential of order α by and establish its inverse along with a detailed description of the associated range space. Our approach employs a wavelet-based method that represents the inverse as the limit of truncated hypersingular integrals parameterized by . To analyze the convergence of these approximations, we introduce the concept of η-smoothness at a point in the Dunkl setting. We show that if a function , for , possesses η-smoothness at , then the truncated hypersingular approximations converge to as .
{"title":"Characterization of bi-parametric potentials and rate of convergence of truncated hypersingular integrals in the Dunkl setting","authors":"Sandeep Kumar Verma, Athulya P","doi":"10.1016/j.jmaa.2026.130499","DOIUrl":"10.1016/j.jmaa.2026.130499","url":null,"abstract":"<div><div>In this work, we introduce the <em>β</em>-semigroup for <span><math><mi>β</mi><mo>></mo><mn>0</mn></math></span>, which unifies and extends the classical Poisson (for <span><math><mi>β</mi><mo>=</mo><mn>1</mn></math></span>) and heat (for <span><math><mi>β</mi><mo>=</mo><mn>2</mn></math></span>) semigroups within the Dunkl analysis framework. Leveraging this semigroup, we derive an explicit representation for the inverse of the Dunkl–Riesz potential and characterize the image of the function space <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn><mi>γ</mi></mrow><mrow><mi>α</mi></mrow></mfrac></math></span>. We further define the bi-parametric potential of order <em>α</em> by<span><span><span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></msubsup><mo>=</mo><msup><mrow><mo>(</mo><mi>I</mi><mo>+</mo><msup><mrow><mo>(</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mrow><mfrac><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mo>−</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mi>β</mi></mrow></mfrac></mrow></msup><mo>,</mo></math></span></span></span> and establish its inverse along with a detailed description of the associated range space. Our approach employs a wavelet-based method that represents the inverse as the limit of truncated hypersingular integrals parameterized by <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>. To analyze the convergence of these approximations, we introduce the concept of <em>η</em>-smoothness at a point <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> in the Dunkl setting. We show that if a function <span><math><mi>f</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>∩</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span>, possesses <em>η</em>-smoothness at <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, then the truncated hypersingular approximations converge to <span><math><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> as <span><math><mi>ϵ</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 2","pages":"Article 130499"},"PeriodicalIF":1.2,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192933","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}
Pub Date : 2026-08-15Epub Date: 2026-02-09DOI: 10.1016/j.jmaa.2026.130495
Azer Khanmamedov , Sema Yayla
In this paper, we consider the initial boundary value problem for the 2D Cahn-Hilliard equation involving inertial and zero-order source terms. In the case when the zero-order source term is a linear function on a large enough neighborhood of the origin, and the coefficient of the inertial term is sufficiently small, we prove that the global attractors for energy and weak solutions coincide. Then, we establish the upper semicontinuity of these global attractors.
{"title":"Upper semicontinuity of global attractors for the generalized Cahn-Hilliard equation with inertial term","authors":"Azer Khanmamedov , Sema Yayla","doi":"10.1016/j.jmaa.2026.130495","DOIUrl":"10.1016/j.jmaa.2026.130495","url":null,"abstract":"<div><div>In this paper, we consider the initial boundary value problem for the 2D Cahn-Hilliard equation involving inertial and zero-order source terms. In the case when the zero-order source term is a linear function on a large enough neighborhood of the origin, and the coefficient of the inertial term is sufficiently small, we prove that the global attractors for energy and weak solutions coincide. Then, we establish the upper semicontinuity of these global attractors.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 2","pages":"Article 130495"},"PeriodicalIF":1.2,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154232","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}
Pub Date : 2026-08-01Epub Date: 2026-02-04DOI: 10.1016/j.jmaa.2026.130488
Xiulan Wu, Fanbo Yu, Xinrui Xu, Jiahui Sun
This paper deals with the initial boundary value problem for a class of coupling Kirchhoff equations with damping term and viscoelastic term. First of all, the local existence and uniqueness of weak solutions are proved by using the Faedo-Galerkin method and the contraction mapping principle. Secondly, we prove the global existence and decay of weak solutions through the method of potential well and the technique of differential inequalities. Finally, we prove the blow-up result of weak solutions under the convex method.
{"title":"Global existence and blow-up of solutions for a class of Kirchhoff coupling systems with damping term","authors":"Xiulan Wu, Fanbo Yu, Xinrui Xu, Jiahui Sun","doi":"10.1016/j.jmaa.2026.130488","DOIUrl":"10.1016/j.jmaa.2026.130488","url":null,"abstract":"<div><div>This paper deals with the initial boundary value problem for a class of coupling Kirchhoff equations with damping term and viscoelastic term. First of all, the local existence and uniqueness of weak solutions are proved by using the Faedo-Galerkin method and the contraction mapping principle. Secondly, we prove the global existence and decay of weak solutions through the method of potential well and the technique of differential inequalities. Finally, we prove the blow-up result of weak solutions under the convex method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130488"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191888","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}
Pub Date : 2026-08-01Epub Date: 2026-02-06DOI: 10.1016/j.jmaa.2026.130493
T.M. Dunster
Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter a and unbounded complex values of the argument. These follow from new Liouville-Green asymptotic expansions for incomplete gamma functions. Asymptotic expansions for the real zeros of the generalised trigonometric integrals are then constructed for large a which are uniformly valid without restriction on their size (small or large).
{"title":"Uniform asymptotic expansions for generalised trigonometric integrals and their zeros","authors":"T.M. Dunster","doi":"10.1016/j.jmaa.2026.130493","DOIUrl":"10.1016/j.jmaa.2026.130493","url":null,"abstract":"<div><div>Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter <em>a</em> and unbounded complex values of the argument. These follow from new Liouville-Green asymptotic expansions for incomplete gamma functions. Asymptotic expansions for the real zeros of the generalised trigonometric integrals are then constructed for large <em>a</em> which are uniformly valid without restriction on their size (small or large).</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130493"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191892","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}
Pub Date : 2026-08-01Epub Date: 2026-02-06DOI: 10.1016/j.jmaa.2026.130494
Jongho Yang
The completeness property of the Nyman-Beurling space is closely related to the Riemann hypothesis. Within this context, we consider the Friedrichs angle between two subspaces of the Nyman-Beurling space. We prove that if the Riemann hypothesis is true, then the Friedrichs angle between the subspaces is zero. Moreover, we present an unexpected result that holds regardless of the truth of the Riemann hypothesis.
{"title":"A Friedrichs angle between the Nyman-Beurling spaces and the Riemann hypothesis","authors":"Jongho Yang","doi":"10.1016/j.jmaa.2026.130494","DOIUrl":"10.1016/j.jmaa.2026.130494","url":null,"abstract":"<div><div>The completeness property of the Nyman-Beurling space is closely related to the Riemann hypothesis. Within this context, we consider the Friedrichs angle between two subspaces of the Nyman-Beurling space. We prove that if the Riemann hypothesis is true, then the Friedrichs angle between the subspaces is zero. Moreover, we present an unexpected result that holds regardless of the truth of the Riemann hypothesis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130494"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191891","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}
Pub Date : 2026-08-01Epub Date: 2026-02-06DOI: 10.1016/j.jmaa.2026.130496
Ruixia Hao , Yunlong Yang
This paper focuses on a class of locally constrained inverse curvature flows for plane curves. This flow exists globally, the evolving curve keeps its length and smoothly converges to a circle centered at the origin as time tends to infinity. As the applications of this flow, we can obtain some geometric inequalities including the classical isoperimetric inequality, curvature-type inequalities, reverse isoperimetric inequality and Chernoff-type inequalities.
{"title":"Locally constrained inverse curvature flows for plane curves and isoperimetric-type inequalities","authors":"Ruixia Hao , Yunlong Yang","doi":"10.1016/j.jmaa.2026.130496","DOIUrl":"10.1016/j.jmaa.2026.130496","url":null,"abstract":"<div><div>This paper focuses on a class of locally constrained inverse curvature flows for plane curves. This flow exists globally, the evolving curve keeps its length and smoothly converges to a circle centered at the origin as time tends to infinity. As the applications of this flow, we can obtain some geometric inequalities including the classical isoperimetric inequality, curvature-type inequalities, reverse isoperimetric inequality and Chernoff-type inequalities.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130496"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191890","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}
Pub Date : 2026-08-01Epub Date: 2026-02-05DOI: 10.1016/j.jmaa.2026.130492
Luis Fernando Mello , Paulo Santana
In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomial or an analytic function. We provide an explicit analytic necessary and sufficient condition for this class of hybrid systems to be asymptotically stable. We also prove the existence of limit cycles in this class of hybrid systems. Our results can be seen as generalizations of results already obtained in the literature. This was possible due to an embedding of piecewise smooth vector fields in a hybrid structure.
{"title":"The hybrid matching of Hurwitz systems","authors":"Luis Fernando Mello , Paulo Santana","doi":"10.1016/j.jmaa.2026.130492","DOIUrl":"10.1016/j.jmaa.2026.130492","url":null,"abstract":"<div><div>In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomial or an analytic function. We provide an explicit analytic necessary and sufficient condition for this class of hybrid systems to be asymptotically stable. We also prove the existence of limit cycles in this class of hybrid systems. Our results can be seen as generalizations of results already obtained in the literature. This was possible due to an embedding of piecewise smooth vector fields in a hybrid structure.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130492"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191938","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}
Pub Date : 2026-08-01Epub Date: 2026-02-03DOI: 10.1016/j.jmaa.2026.130487
Qiyu Yang , Shengbo Zhao
In this paper, we establish lower bounds for the maximum of derivatives of the Riemann zeta function on vertical homogeneous progressions. When the real part σ lies within a suitable range, we show that the discrete case has a similar order of magnitude to the continuous case, using the resonance method.
{"title":"Large values of derivatives of the Riemann zeta function on vertical homogeneous progressions","authors":"Qiyu Yang , Shengbo Zhao","doi":"10.1016/j.jmaa.2026.130487","DOIUrl":"10.1016/j.jmaa.2026.130487","url":null,"abstract":"<div><div>In this paper, we establish lower bounds for the maximum of derivatives of the Riemann zeta function on vertical homogeneous progressions. When the real part <em>σ</em> lies within a suitable range, we show that the discrete case has a similar order of magnitude to the continuous case, using the resonance method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130487"},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191939","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}
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