Journal of Differential Equations最新文献

Global L∞ entropy solutions to system of polytropic gas dynamics with a source 带源多向气体动力学系统的全局L∞熵解

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-21 DOI: 10.1016/j.jde.2025.113630

J.J Chen , Q.Q. Fang , C. Klingenberg , Y.-G. Lu , X.X Tao , N. Tsuge

{"title":"Global L∞ entropy solutions to system of polytropic gas dynamics with a source","authors":"J.J Chen , Q.Q. Fang , C. Klingenberg , Y.-G. Lu , X.X Tao , N. Tsuge","doi":"10.1016/j.jde.2025.113630","DOIUrl":"10.1016/j.jde.2025.113630","url":null,"abstract":"<div><div>In this paper, we study the global <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> entropy solutions for the Cauchy problem of the polytropic gas dynamics system in a general nozzle with friction. First, under bounded conditions on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the cross-sectional area function <span><math><mi>A</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> and the friction function <span><math><mi>α</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, we apply the flux-approximation technique coupled with the classical viscosity method to obtain the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> estimates of the viscosity-flux approximate solutions for any exponent <span><math><mi>γ</mi><mo>≥</mo><mn>1</mn></math></span>; Second, by using the compactness framework from the compensated compactness theory, we prove the convergence of the viscosity-flux approximate solutions and obtain the global existence of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> entropy solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113630"},"PeriodicalIF":2.4,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672121","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 speed for some cooperative systems with nonlocal diffusion and free boundaries, part 2: Precise rates of acceleration 一类具有非局部扩散和自由边界的合作系统的扩散速度，第2部分：精确加速度

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-18 DOI: 10.1016/j.jde.2025.113624

Yihong Du , Wenjie Ni , Rong Wang

{"title":"Spreading speed for some cooperative systems with nonlocal diffusion and free boundaries, part 2: Precise rates of acceleration","authors":"Yihong Du , Wenjie Ni , Rong Wang","doi":"10.1016/j.jde.2025.113624","DOIUrl":"10.1016/j.jde.2025.113624","url":null,"abstract":"<div><div>We investigate a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and some of the equations in the system do not have a diffusion term. Such a system covers various models arising from population biology and epidemiology, including in particular a West Nile virus model <span><span>[12]</span></span> and an epidemic model <span><span>[38]</span></span>, where a “spreading-vanishing” dichotomy is known to govern the long time dynamical behaviour, but the spreading rate was not well understood. We aim to develop a systematic approach to determine the spreading profile of the system. In an earlier work <span><span>[13]</span></span>, we obtained threshold conditions on the kernel functions which decide exactly when the spreading has finite speed, or infinite speed (accelerated spreading), and for the case of finite speed, we determined its value via semi-wave solutions. In the current work, we focus on the case of accelerated spreading, and obtain the precise rates of acceleration for some typical classes of kernel functions. Our results apply directly to the above mentioned concrete models.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113624"},"PeriodicalIF":2.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656736","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

Global multiplicity results in a Moore–Nehari type problem with a spectral parameter 全局多重性导致一个具有谱参数的Moore-Nehari型问题

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-18 DOI: 10.1016/j.jde.2025.113628

Julián López-Gómez , Eduardo Muñoz-Hernández , Fabio Zanolin

{"title":"Global multiplicity results in a Moore–Nehari type problem with a spectral parameter","authors":"Julián López-Gómez , Eduardo Muñoz-Hernández , Fabio Zanolin","doi":"10.1016/j.jde.2025.113628","DOIUrl":"10.1016/j.jde.2025.113628","url":null,"abstract":"<div><div>This paper analyzes the structure of the set of positive solutions of <span><span>(1.1)</span></span>, where <span><math><mi>a</mi><mo>≡</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> is the piece-wise constant function defined in <span><span>(1.3)</span></span> for some <span><math><mi>h</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. In our analysis, <em>λ</em> is regarded as a bifurcation parameter, whereas <em>h</em> is viewed as a deformation parameter between the autonomous case when <span><math><mi>a</mi><mo>=</mo><mn>1</mn></math></span> and the linear case when <span><math><mi>a</mi><mo>=</mo><mn>0</mn></math></span>. In this paper, besides establishing some of the multiplicity results suggested by the numerical experiments of <span><span>[2]</span></span>, we have analyzed the asymptotic behavior of the positive solutions of <span><span>(1.1)</span></span> as <span><math><mi>h</mi><mo>↑</mo><mn>1</mn></math></span>, when the shadow system of <span><span>(1.1)</span></span> is the linear equation <span><math><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>=</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span>. This is the first paper where such a problem has been addressed. Numerics is of no help in analyzing this singular perturbation problem because the positive solutions blow-up point-wise in <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> as <span><math><mi>h</mi><mo>↑</mo><mn>1</mn></math></span> if <span><math><mi>λ</mi><mo><</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113628"},"PeriodicalIF":2.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656737","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

Nonlinear Schrödinger-Poisson systems in dimension two: The zero mass case 二维非线性Schrödinger-Poisson系统：零质量情况

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-18 DOI: 10.1016/j.jde.2025.113633

Federico Bernini , Giulio Romani , Cristina Tarsi

{"title":"Nonlinear Schrödinger-Poisson systems in dimension two: The zero mass case","authors":"Federico Bernini , Giulio Romani , Cristina Tarsi","doi":"10.1016/j.jde.2025.113633","DOIUrl":"10.1016/j.jde.2025.113633","url":null,"abstract":"<div><div>We provide an existence result for a Schrödinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev embedding, we admit nonlinearities with subcritical or critical growth in the sense of Trudinger-Moser. In particular, the absence of the mass term requires a nonstandard functional framework, based on homogeneous Sobolev spaces. These features, combined with the logarithmic behaviour of the kernel of the Poisson equation, make the analysis delicate, since standard variational tools cannot be applied. The system is solved by considering the corresponding logarithmic Choquard equation. The existence of a mountain pass-type solution is established by means of a careful analysis of appropriate Cerami sequences, whose boundedness is ensured through a nonstandard variational method, suggested by the subtle nature of the functional geometry involved. As a key tool in our estimates, we also introduce a logarithmic weighted Trudinger–Moser inequality, along with a related Cao-type inequality, both of which hold in our functional setting and are, we believe, of independent interest.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113633"},"PeriodicalIF":2.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656738","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

Controllability of impulsive differential inclusions with nonlocal condition driven by hemivariational inequalities 半分不等式驱动非局部条件下脉冲微分包体的可控性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-17 DOI: 10.1016/j.jde.2025.113622

Akhilesh Verma, Jaydev Dabas

引用次数: 0

Uniqueness and multiplicity of positive radial solutions to the super-critical Brezis-Nirenberg problem in an annulus 环空超临界Brezis-Nirenberg问题径向正解的唯一性和多重性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-17 DOI: 10.1016/j.jde.2025.113621

Naoki Shioji , Satoshi Tanaka , Kohtaro Watanabe

引用次数: 0

Energy transport in random perturbations of mechanical systems 机械系统随机扰动中的能量输运

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-17 DOI: 10.1016/j.jde.2025.113619

Anna Maria Cherubini , Marian Gidea

引用次数: 0

Asymptotic stability of the equilibrium for the free boundary problem of a compressible atmospheric primitive model with physical vacuum 具有物理真空的可压缩大气原始模型自由边界问题平衡的渐近稳定性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-17 DOI: 10.1016/j.jde.2025.113620

Xin Liu , Edriss S. Titi , Zhouping Xin

引用次数: 0

Global existence for Lotka-Volterra models of predation and competition with diffusion and predator/competitor taxis in the spatial dimension n = 2,3 空间维度n上具有扩散和捕食者/竞争者的士的捕食与竞争Lotka-Volterra模型的全局存在性 = 2,3

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-16 DOI: 10.1016/j.jde.2025.113625

Purnedu Mishra , Dariusz Wrzosek

{"title":"Global existence for Lotka-Volterra models of predation and competition with diffusion and predator/competitor taxis in the spatial dimension n = 2,3","authors":"Purnedu Mishra , Dariusz Wrzosek","doi":"10.1016/j.jde.2025.113625","DOIUrl":"10.1016/j.jde.2025.113625","url":null,"abstract":"<div><div>We study a prey-predator system and the competition system, both with Lotka-Volterra reaction terms, assuming, in addition to the diffusive movement of both species, an avoidance strategy of one of them modeled as repulsive taxis. For the predator-prey case, also called predator-taxis, the global existence of classical solutions is proven for the 2D case, assuming prey density dependent velocity suppression whose strength depends on some parameter <em>σ</em> - an assumption unnecessary in the prey-taxis case, whose role is confirmed by numerical simulations presented in the paper. This assumption is also useful in proving global classical solutions to the 3D competition model with competitor-taxis and the velocity suppression; it also serves as a regularization of the original model, which allows us to prove in the limit, <span><math><mi>σ</mi><mo>→</mo><mn>0</mn></math></span>, the existence of weak distributional solutions to the 3D competition model. The velocity suppression turns out to be unnecessary assumption to prevent blow-up of solutions to the competition model with competitor-taxis in 2D case. Finally, we emphasize that our numerical simulations starting from appropriately selected initial conditions, in addition to their illustrative function, indicate directions for further research.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113625"},"PeriodicalIF":2.4,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633369","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

Co-existence of planar and non-planar traveling waves in a sharp interface model 平面行波与非平面行波在锐界面模型中的共存

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-07-16 DOI: 10.1016/j.jde.2025.113615

Chao-Nien Chen , Yung-Sze Choi , Nicola Fusco

引用次数: 0