Journal of Differential Equations最新文献_第9页

On the sharp Hessian integrability conjecture in the plane 关于平面中的尖锐黑森可整性猜想

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-14 DOI: 10.1016/j.jde.2024.10.001

Thialita M. Nascimento, Eduardo V. Teixeira

引用次数: 0

On the Cauchy problem for a combined mCH-Novikov integrable equation with linear dispersion 关于具有线性分散性的 mCH-Novikov 组合可积分方程的考奇问题

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-14 DOI: 10.1016/j.jde.2024.09.030

Zhenyu Wan , Ying Wang , Min Zhu

{"title":"On the Cauchy problem for a combined mCH-Novikov integrable equation with linear dispersion","authors":"Zhenyu Wan , Ying Wang , Min Zhu","doi":"10.1016/j.jde.2024.09.030","DOIUrl":"10.1016/j.jde.2024.09.030","url":null,"abstract":"<div><div>This paper aims to understand a blow-up mechanism on a family of shallow-water models with linear dispersion, which are linked with the modified Camassa-Holm equation and the Novikov equation. We first demonstrate the local well-posedness of the model equation in Besov spaces. Our blow-up analysis begins with two cases where the first case is <span><math><mn>2</mn><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mn>3</mn><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn></math></span> and then we deduce the results on the curvature blow-up in finite time. To overcome the lack of conservation in the functional due to weak linear dispersion, we can determine a suitable alternative via a slight modification to conserved quantity <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>[</mo><mi>u</mi><mo>]</mo></math></span> (see <span><span>Lemma 4.1</span></span>). Furthermore, we explore the formation of singularities in another case when nonlocal terms are absent. Lastly, we investigate the Gevrey regularity and analyticity of solutions for Cauchy problem within a specified range of Gevrey-Sobolev spaces by employing the generalized Ovsyannikov theorem and study the continuity of the data-to-solution mapping.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 727-767"},"PeriodicalIF":2.4,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432940","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}

引用次数: 0

On some regularity properties of mixed local and nonlocal elliptic equations 论混合局部和非局部椭圆方程的一些正则特性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-14 DOI: 10.1016/j.jde.2024.10.003

Xifeng Su , Enrico Valdinoci , Yuanhong Wei , Jiwen Zhang

{"title":"On some regularity properties of mixed local and nonlocal elliptic equations","authors":"Xifeng Su , Enrico Valdinoci , Yuanhong Wei , Jiwen Zhang","doi":"10.1016/j.jde.2024.10.003","DOIUrl":"10.1016/j.jde.2024.10.003","url":null,"abstract":"<div><div>This article is concerned with “up to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity results” about a mixed local-nonlocal nonlinear elliptic equation which is driven by the superposition of Laplacian and fractional Laplacian operators.</div><div>First of all, an estimate on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm of weak solutions is established for more general cases than the ones present in the literature, including here critical nonlinearities.</div><div>We then prove the interior <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity up to the boundary of weak solutions, which extends previous results by the authors (Su et al., 2022, <span><span>[20]</span></span>), where the nonlinearities considered were of subcritical type.</div><div>In addition, we establish the interior <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity of solutions for all <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity up to the boundary for all <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></math></span>, with sharp regularity exponents.</div><div>For further perusal, we also include a strong maximum principle and some properties about the principal eigenvalue.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 576-613"},"PeriodicalIF":2.4,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432942","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}

引用次数: 0

Dynamics of classical solutions to a diffusive epidemic model with varying population demographics 具有不同人口结构的扩散性流行病模型经典解的动态变化

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-10 DOI: 10.1016/j.jde.2024.09.058

T.J. Doumatè , J. Kotounou , L.A. Leadi , R.B. Salako

{"title":"Dynamics of classical solutions to a diffusive epidemic model with varying population demographics","authors":"T.J. Doumatè , J. Kotounou , L.A. Leadi , R.B. Salako","doi":"10.1016/j.jde.2024.09.058","DOIUrl":"10.1016/j.jde.2024.09.058","url":null,"abstract":"<div><div>We study the asymptotic dynamics of solutions to a diffusive epidemic model with varying population dynamics. The large-time behavior of solutions is completely described in spatially homogeneous environments. When the environment is spatially heterogeneous, it is shown that there exist two critical numbers <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>≤</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo><</mo><mo>∞</mo></math></span> such that if the ratio <span><math><mfrac><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac></math></span> of the infected population diffusion rate and the susceptible population rate either exceeds <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> or is less than <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span>, then the epidemic model has an endemic equilibrium (EE) solution if and only if the basic reproduction number (BRN) exceeds one. The unique EE is non-degenerate if <span><math><mfrac><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac><mo>≥</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. Furthermore, results on the global dynamics of solutions are established when <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mn>1</mn></math></span>. Our results shed some light on the differences on disease predictions for constant total population size models versus varying population size models. Results on the asymptotic profiles of the EEs for small population diffusion rates are also established.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 491-530"},"PeriodicalIF":2.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425004","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}

引用次数: 0

The massless Dirac equation in three dimensions: Dispersive estimates and zero energy obstructions 三维空间中的无质量狄拉克方程：分散估计和零能量障碍

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-09 DOI: 10.1016/j.jde.2024.10.005

William R. Green , Connor Lane , Benjamin Lyons , Shyam Ravishankar , Aden Shaw

{"title":"The massless Dirac equation in three dimensions: Dispersive estimates and zero energy obstructions","authors":"William R. Green , Connor Lane , Benjamin Lyons , Shyam Ravishankar , Aden Shaw","doi":"10.1016/j.jde.2024.10.005","DOIUrl":"10.1016/j.jde.2024.10.005","url":null,"abstract":"<div><div>We investigate dispersive estimates for the massless three dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a <span><math><msup><mrow><mo>〈</mo><mi>t</mi><mo>〉</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> decay rate as an operator from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> regardless of the existence of zero energy eigenfunctions. We also show this decay rate may be improved to <span><math><msup><mrow><mo>〈</mo><mi>t</mi><mo>〉</mo></mrow><mrow><mo>−</mo><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup></math></span> for any <span><math><mn>0</mn><mo>≤</mo><mi>γ</mi><mo><</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> at the cost of spatial weights. This estimate, along with the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> conservation law allows one to deduce a family of Strichartz estimates in the case of a threshold eigenvalue. We classify the structure of threshold obstructions as being composed of zero energy eigenfunctions. Finally, we show the Dirac evolution is bounded for all time with minimal requirements on the decay of the potential and smoothness of initial data.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 449-490"},"PeriodicalIF":2.4,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425003","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}

引用次数: 0

Spreading properties for a predator-prey system with nonlocal dispersal and climate change 具有非本地传播和气候变化的捕食者-猎物系统的传播特性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-08 DOI: 10.1016/j.jde.2024.09.057

Rong Zhou, Shi-Liang Wu

{"title":"Spreading properties for a predator-prey system with nonlocal dispersal and climate change","authors":"Rong Zhou, Shi-Liang Wu","doi":"10.1016/j.jde.2024.09.057","DOIUrl":"10.1016/j.jde.2024.09.057","url":null,"abstract":"<div><div>In this paper, we investigate the spreading properties for a predator-prey system with nonlocal dispersal and climate change. We are concerned with the case when the prey grow relatively rapidly at one side of the habitat and grow relatively slowly at another side of the habitat. We are interested in the effect of the climate change on the spreading speed of the predator and prey. In the case where the predator is faster than the prey, we show that the predator and the prey have the same leftward spreading speed and the same rightward spreading speed, respectively, which depend on <em>c</em>, the climate change speed, and <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mo>±</mo><mo>∞</mo><mo>)</mo></math></span>, the maximum and minimum speeds of the prey without predator. While in the case where the prey is faster than the predator, we find that the solution can form a multi-layer wave and the two species have different leftward spreading speeds and different rightward spreading speeds, which depend on <em>c</em>, <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mo>±</mo><mo>∞</mo><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mo>±</mo><mo>∞</mo><mo>)</mo></math></span>, the maximum and minimum speeds of the predator when the density of the prey attains its maximum and minimum capacity.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"415 ","pages":"Pages 791-828"},"PeriodicalIF":2.4,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417322","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}

引用次数: 0

Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion 使具有混合分散性的薛定谔型系统的解规范不敏感的控制方法

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-04 DOI: 10.1016/j.jde.2024.09.054

Roberto de A. Capistrano–Filho , Thiago Yukio Tanaka

引用次数: 0

Global existence of strong solutions to the compressible magnetohydrodynamic equations with large initial data and vacuum in R2 R2 中具有大初始数据和真空的可压缩磁流体动力学方程强解的全局存在性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-04 DOI: 10.1016/j.jde.2024.09.056

Xue Wang, Xiaojing Xu

{"title":"Global existence of strong solutions to the compressible magnetohydrodynamic equations with large initial data and vacuum in R2","authors":"Xue Wang, Xiaojing Xu","doi":"10.1016/j.jde.2024.09.056","DOIUrl":"10.1016/j.jde.2024.09.056","url":null,"abstract":"<div><div>This paper concerns the Cauchy problem to the compressible magnetohydrodynamic equations in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with the constant state of density at far field being vacuum or nonvacuum. Under the conditions that the adiabatic constant <span><math><mi>γ</mi><mo>></mo><mn>1</mn></math></span>, the shear viscosity coefficient <em>μ</em> is a positive constant, and the bulk one <span><math><mi>λ</mi><mo>(</mo><mi>ρ</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span> with <span><math><mi>β</mi><mo>></mo><mn>4</mn><mo>/</mo><mn>3</mn></math></span>, we establish the global existence and uniqueness of strong solutions. In particular, the initial data can be arbitrarily large and the density is allowed to vanish initially. These results generalize and improve previous ones by Huang-Li (2022) and Jiu-Wang-Xin (2018) for compressible Navier-Stokes equations. This paper introduces some key weighted estimates on <em>H</em> and presents some delicate analysis to exploit the decay properties of solutions due to the strong coupling and interplay interaction.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"415 ","pages":"Pages 722-763"},"PeriodicalIF":2.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417303","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}

引用次数: 0

Minkowski problems arise from sub-linear elliptic equations 亚线性椭圆方程引发的闵科夫斯基问题

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-04 DOI: 10.1016/j.jde.2024.09.023

Qiuyi Dai, Xing Yi

引用次数: 0

Large deviation principle for multi-scale fully local monotone stochastic dynamical systems with multiplicative noise 具有乘法噪声的多尺度完全局部单调随机动力系统的大偏差原理

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-10-04 DOI: 10.1016/j.jde.2024.09.059

Wei Hong, Wei Liu, Luhan Yang

引用次数: 0