Pub Date : 2026-05-25Epub Date: 2026-02-06DOI: 10.1016/j.jde.2026.114187
Jie Guo, Quansen Jiu
In this paper, we study the generalized Proudman-Johnson equation posed on the torus. In the critical regime where the parameter a is close to and slightly greater than 1, we establish finite time blow-up of smooth solutions to the inviscid case. Moreover, we show that the blow-up is asymptotically self-similar for a class of smooth initial data. In contrast, when the parameter a lies slightly below 1, we prove the global in time existence for the same initial data. In addition, we demonstrate that inviscid Proudman-Johnson equation with Hölder continuous data also develops a self-similar blow-up. Finally, for the viscous case with , we prove that smooth initial data can still lead to finite time blow-up.
{"title":"Finite time blow-up analysis for the generalized Proudman-Johnson model","authors":"Jie Guo, Quansen Jiu","doi":"10.1016/j.jde.2026.114187","DOIUrl":"10.1016/j.jde.2026.114187","url":null,"abstract":"<div><div>In this paper, we study the generalized Proudman-Johnson equation posed on the torus. In the critical regime where the parameter <em>a</em> is close to and slightly greater than 1, we establish finite time blow-up of smooth solutions to the inviscid case. Moreover, we show that the blow-up is asymptotically self-similar for a class of smooth initial data. In contrast, when the parameter <em>a</em> lies slightly below 1, we prove the global in time existence for the same initial data. In addition, we demonstrate that inviscid Proudman-Johnson equation with Hölder continuous data also develops a self-similar blow-up. Finally, for the viscous case with <span><math><mi>a</mi><mo>></mo><mn>1</mn></math></span>, we prove that smooth initial data can still lead to finite time blow-up.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114187"},"PeriodicalIF":2.3,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-25Epub Date: 2026-02-06DOI: 10.1016/j.jde.2026.114192
Qi Xiong , Zhenqiu Zhang , Lingwei Ma
In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the regularity criterion.
{"title":"Riesz potential estimates for double obstacle problems with Orlicz growth","authors":"Qi Xiong , Zhenqiu Zhang , Lingwei Ma","doi":"10.1016/j.jde.2026.114192","DOIUrl":"10.1016/j.jde.2026.114192","url":null,"abstract":"<div><div>In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> regularity criterion.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114192"},"PeriodicalIF":2.3,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-25Epub Date: 2026-02-10DOI: 10.1016/j.jde.2026.114195
Soobin Cho, Renming Song
<div><div>Assume <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. Let <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> be the generator of a symmetric, but not necessarily isotropic, <em>α</em>-stable process <em>X</em> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> whose Lévy density is comparable with that of an isotropic <em>α</em>-stable process. In this paper, we show that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> regularity assumption on an open set <span><math><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> is optimal for the standard boundary decay property of nonnegative <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-harmonic functions in <em>D</em>, and for the standard boundary decay property of the heat kernel <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>D</mi></mrow></msup><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> of the part process <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>D</mi></mrow></msup></math></span> of <em>X</em> on <em>D</em> by proving the following: (i) If <em>D</em> is a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open set and <em>h</em> is a nonnegative function which is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-harmonic in <em>D</em> and vanishes near a portion of ∂<em>D</em>, then the rate at which <span><math><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> decays to 0 near that portion of ∂<em>D</em> is <span><math><mrow><mi>dist</mi></mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span>. (ii) If <em>D</em> is a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open set, then, as <span><math><mi>x</mi><mo>→</mo><mo>∂</mo><mi>D</mi></math></span>, the rate at which <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>D</mi></mrow></msup><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> tends to 0 is <span><math><mrow><mi>dist</mi></mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span>. (iii) For any non-Dini modulus of continuity <em>ℓ</em>, there exist non-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open sets <em>D</em>, with ∂<em>D</em>
{"title":"Abnormal boundary decay for stable operators","authors":"Soobin Cho, Renming Song","doi":"10.1016/j.jde.2026.114195","DOIUrl":"10.1016/j.jde.2026.114195","url":null,"abstract":"<div><div>Assume <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. Let <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> be the generator of a symmetric, but not necessarily isotropic, <em>α</em>-stable process <em>X</em> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> whose Lévy density is comparable with that of an isotropic <em>α</em>-stable process. In this paper, we show that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> regularity assumption on an open set <span><math><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> is optimal for the standard boundary decay property of nonnegative <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-harmonic functions in <em>D</em>, and for the standard boundary decay property of the heat kernel <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>D</mi></mrow></msup><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> of the part process <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>D</mi></mrow></msup></math></span> of <em>X</em> on <em>D</em> by proving the following: (i) If <em>D</em> is a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open set and <em>h</em> is a nonnegative function which is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-harmonic in <em>D</em> and vanishes near a portion of ∂<em>D</em>, then the rate at which <span><math><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> decays to 0 near that portion of ∂<em>D</em> is <span><math><mrow><mi>dist</mi></mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span>. (ii) If <em>D</em> is a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open set, then, as <span><math><mi>x</mi><mo>→</mo><mo>∂</mo><mi>D</mi></math></span>, the rate at which <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>D</mi></mrow></msup><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> tends to 0 is <span><math><mrow><mi>dist</mi></mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span>. (iii) For any non-Dini modulus of continuity <em>ℓ</em>, there exist non-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mrow><mi>Dini</mi></mrow></mrow></msup></math></span> open sets <em>D</em>, with ∂<em>D</em> ","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114195"},"PeriodicalIF":2.3,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-25Epub Date: 2026-02-10DOI: 10.1016/j.jde.2026.114194
Fan Xu, Lei Zhang, Bin Liu
In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains , . Our main results are summarized as follows. For and , we establish the existence and uniqueness of a local-in-time pathwise weak solution. For and , we prove the existence and uniqueness of a global-in-time pathwise weak solution together with at least one invariant measure. For and , we obtain the existence and uniqueness of a global-in-time pathwise very weak solution and at least one invariant measure, while for we establish only the existence of a martingale solution due to the loss of pathwise uniqueness.
{"title":"Well-posedness and invariant measures for the stochastically perturbed Landau-Lifshitz-Baryakhtar equation","authors":"Fan Xu, Lei Zhang, Bin Liu","doi":"10.1016/j.jde.2026.114194","DOIUrl":"10.1016/j.jde.2026.114194","url":null,"abstract":"<div><div>In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains <span><math><mi>O</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>. Our main results are summarized as follows. For <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>, we establish the existence and uniqueness of a local-in-time pathwise weak solution. For <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><mi>d</mi><mo>=</mo><mn>1</mn></math></span>, we prove the existence and uniqueness of a global-in-time pathwise weak solution together with at least one invariant measure. For <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span>, we obtain the existence and uniqueness of a global-in-time pathwise very weak solution and at least one invariant measure, while for <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span> we establish only the existence of a martingale solution due to the loss of pathwise uniqueness.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114194"},"PeriodicalIF":2.3,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-25Epub Date: 2026-02-10DOI: 10.1016/j.jde.2026.114196
Wencai Liu , Matthew Powell , Yiding Max Tang , Xueyin Wang , Ruixiang Zhang , Justin Zhou
We establish asymptotically sharp semi-algebraic discrepancy estimates for multi-frequency shift sequences. As an application, we obtain novel upper bounds for the quantum dynamics of long-range quasi-periodic Schrödinger operators.
{"title":"Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics","authors":"Wencai Liu , Matthew Powell , Yiding Max Tang , Xueyin Wang , Ruixiang Zhang , Justin Zhou","doi":"10.1016/j.jde.2026.114196","DOIUrl":"10.1016/j.jde.2026.114196","url":null,"abstract":"<div><div>We establish asymptotically sharp semi-algebraic discrepancy estimates for multi-frequency shift sequences. As an application, we obtain novel upper bounds for the quantum dynamics of long-range quasi-periodic Schrödinger operators.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114196"},"PeriodicalIF":2.3,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-15Epub Date: 2026-01-28DOI: 10.1016/j.jde.2026.114140
Fan Bu, Dachun Yang, Wen Yuan, Mingdong Zhang
Using growth functions, we introduce generalized matrix-weighted Besov–Triebel–Lizorkin-type spaces with matrix weights. We first characterize these spaces, respectively, in terms of the φ-transform, the Peetre-type maximal function, and the Littlewood–Paley functions. Furthermore, after establishing the boundedness of almost diagonal operators on the corresponding sequence spaces, we obtain the molecular and the wavelet characterizations of these spaces. As applications, we find the sufficient and necessary conditions for the invariance of those Triebel–Lizorkin-type spaces on the integrable index and also for the Sobolev-type embedding of all these spaces. The main novelty exists in that these results are of wide generality, the growth condition of growth functions is not only sufficient but also necessary for the boundedness of almost diagonal operators and hence this new framework of Besov–Triebel–Lizorkin-type is optimal, some results either are new or improve the known ones even for known matrix-weighted Besov–Triebel–Lizorkin spaces, and, furthermore, even in the scalar-valued setting, all the results are also new.
{"title":"Matrix-weighted Besov–Triebel–Lizorkin spaces of optimal scale: Real-variable characterizations, invariance on integrable index, and Sobolev-type embedding","authors":"Fan Bu, Dachun Yang, Wen Yuan, Mingdong Zhang","doi":"10.1016/j.jde.2026.114140","DOIUrl":"10.1016/j.jde.2026.114140","url":null,"abstract":"<div><div>Using growth functions, we introduce generalized matrix-weighted Besov–Triebel–Lizorkin-type spaces with matrix <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> weights. We first characterize these spaces, respectively, in terms of the <em>φ</em>-transform, the Peetre-type maximal function, and the Littlewood–Paley functions. Furthermore, after establishing the boundedness of almost diagonal operators on the corresponding sequence spaces, we obtain the molecular and the wavelet characterizations of these spaces. As applications, we find the sufficient and necessary conditions for the invariance of those Triebel–Lizorkin-type spaces on the integrable index and also for the Sobolev-type embedding of all these spaces. The main novelty exists in that these results are of wide generality, the growth condition of growth functions is not only sufficient but also necessary for the boundedness of almost diagonal operators and hence this new framework of Besov–Triebel–Lizorkin-type is optimal, some results either are new or improve the known ones even for known matrix-weighted Besov–Triebel–Lizorkin spaces, and, furthermore, even in the scalar-valued setting, all the results are also new.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"463 ","pages":"Article 114140"},"PeriodicalIF":2.3,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-15Epub Date: 2026-01-28DOI: 10.1016/j.jde.2026.114167
Qunyi Bie , Hui Fang , Shu Wang , Yanping Zhou
This paper aims to study the global stability and long-time behavior of the three-dimensional incompressible anisotropic Navier-Stokes equations with only fractional horizontal dissipation. The absence of vertical dissipation induces substantial analytical difficulties, rendering classical methods such as Schonbek's Fourier splitting technique inapplicable. By developing refined anisotropic energy estimates that exploit both the divergence-free condition and the structure of the dissipation, we establish the global existence and asymptotic stability of small solutions in Sobolev spaces under weaker dissipation conditions than previously known. Furthermore, for suitably regular initial data, we prove sharp decay rates for the solution and its first-order derivatives. Our results substantially enlarge the admissible parameter regime and provide robust analytical tools that may also be applied to other fractional anisotropic fluid models.
{"title":"Stability and sharp decay for the 3D incompressible anisotropic Navier-Stokes equations with fractional horizontal dissipation","authors":"Qunyi Bie , Hui Fang , Shu Wang , Yanping Zhou","doi":"10.1016/j.jde.2026.114167","DOIUrl":"10.1016/j.jde.2026.114167","url":null,"abstract":"<div><div>This paper aims to study the global stability and long-time behavior of the three-dimensional incompressible anisotropic Navier-Stokes equations with only fractional horizontal dissipation. The absence of vertical dissipation induces substantial analytical difficulties, rendering classical methods such as Schonbek's Fourier splitting technique inapplicable. By developing refined anisotropic energy estimates that exploit both the divergence-free condition and the structure of the dissipation, we establish the global existence and asymptotic stability of small solutions in Sobolev spaces under weaker dissipation conditions than previously known. Furthermore, for suitably regular initial data, we prove sharp decay rates for the solution and its first-order derivatives. Our results substantially enlarge the admissible parameter regime and provide robust analytical tools that may also be applied to other fractional anisotropic fluid models.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"463 ","pages":"Article 114167"},"PeriodicalIF":2.3,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-05Epub Date: 2026-01-23DOI: 10.1016/j.jde.2026.114133
Youjun Deng , Lingzheng Kong , Yongjian Liu , Liyan Zhu
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of N-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an N-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the N-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings.
{"title":"Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures","authors":"Youjun Deng , Lingzheng Kong , Yongjian Liu , Liyan Zhu","doi":"10.1016/j.jde.2026.114133","DOIUrl":"10.1016/j.jde.2026.114133","url":null,"abstract":"<div><div>Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of <em>N</em>-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an <em>N</em>-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an <span><math><mi>N</mi><mo>×</mo><mi>N</mi></math></span> tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the <em>N</em>-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114133"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-05Epub Date: 2026-02-26DOI: 10.1016/j.jde.2026.114249
P.L. Robinson
We study quartic counterparts to the elliptic functions sm and cm of A.C. Dixon.
研究了狄克逊椭圆函数sm和cm的四次对应物。
{"title":"Quartic dixonians","authors":"P.L. Robinson","doi":"10.1016/j.jde.2026.114249","DOIUrl":"10.1016/j.jde.2026.114249","url":null,"abstract":"<div><div>We study quartic counterparts to the elliptic functions sm and cm of A.C. Dixon.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114249"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-05Epub Date: 2026-01-23DOI: 10.1016/j.jde.2026.114131
Jussi Behrndt , Fritz Gesztesy , Seppo Hassi , Roger Nichols , Henk de Snoo
Any self-adjoint extension of a (singular) Sturm–Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm–Liouville operator by using generalized boundary values. We provide these forms in detail in all possible cases (explicitly, when both endpoints are limit circle, when one endpoint is limit circle, and when both endpoints are limit point).
{"title":"On sesquilinear forms for lower semibounded (singular) Sturm–Liouville operators","authors":"Jussi Behrndt , Fritz Gesztesy , Seppo Hassi , Roger Nichols , Henk de Snoo","doi":"10.1016/j.jde.2026.114131","DOIUrl":"10.1016/j.jde.2026.114131","url":null,"abstract":"<div><div>Any self-adjoint extension of a (singular) Sturm–Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm–Liouville operator by using generalized boundary values. We provide these forms in detail in all possible cases (explicitly, when both endpoints are limit circle, when one endpoint is limit circle, and when both endpoints are limit point).</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114131"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号