检索结果-南通市图书馆

A critical Trudinger-Moser inequality involving a degenerate potential and nonlinear Schrodinger equations

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2021年第7期64卷 1391-1410页

作者： Lu Chen Guozhen Lu maochun zhu School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Department of Mathematics University of ConnecticutStorrsCT 06269USA School of Mathematical Sciences Institute of Applied System AnalysisJiangsu UniversityZhenjiang 212013China

The classical critical Trudinger-Moser inequality in R^(2)under the constraint∫_(R_(2))(|▽u|^(2)+|u|^(2))dx≤1 was established through the technique of blow-up analysis or the rearrangement-free argument:for anyτ>0,it holds that sup u∈H^(1)(r^(2)fR^(2)(τ|U|^(2)+|▽u|^(2)dx≤1∫_(R^(2)(E^4π|u|^(2)-1)dx≤C(τ)<+∞)))and 4πis ***,if we consider the less restrictive constraint∫_(R_(2))(|▽u|^(2)+|u|^(2))dx≤1,where V(x)is nonnegative and vanishes on an open set in R^(2),it is unknown whether the sharp constant of the Trudinger-Moser inequality is still 4π.The loss of a positive lower bound of the potential V(x)makes this problem become fairly *** main purpose of this paper is *** will first establish the Trudinger-Moser inequality sup u∈H^(1)(r^(2)fR^(2)(τ|U|^(2)+|▽u|^(2)dx≤1∫_(R^(2)(E^4π|u|^(2)-1)dx≤C(τ)<+∞)))when V is nonnegative and vanishes on an open set in R^(2).As an application,we also prove the existence of ground state solutions to the following Sciridinger equations with critical exponeitial growth:-Δu+V(x)u=f u)in R^(2),(0.1)where V(x)≥0 and vanishes on an open set of R^(2)and f has critical exponential *** a positive constant lower bound for the potential V(x)(e.g.,the Rabinowitz type potential)has been the standard assumption when one deals with the existence of solutions to the above Schrodinger equations when the nonlinear term has the exponential *** existence result seems to be the first one without this standard assumption.

关键词： Trudinger-Moser inequalities degenerate potential ground state solutions Schrodinger equations Nehari manifold

Trudinger-Moser Type Inequality Under Lorentz-Sobolev Norms Constraint

在线全文

学校读者我要写书评

暂无评论

Journal of Partial Differential Equations 2021年第2期34卷 116-128页

作者： zhu maochun ZHENG Yifeng School of Mathematical Sciences Institute of Applied System AnalysisJiangsu UniversityZhenjiang 212013China

In this paper,we are concerned with a sharp fractional Trudinger-Moser type inequality in bounded intervals of IR under the Lorentz-Sobolev norms *** any 1β***,when q is even,we obtain u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ih(u)eβq|u(x)|q')dx≤+∞),for any function h:[0,∞→[0,∞)with lim t→∞h(t)=∞.As for the key tools of proof,we use Green functions for fractional Laplace operators and the rearrangement of a convolution to the rearrangement of the convoluted functions.

关键词： Trudinger-Moser inequality Lorentz-Sobolev space bounded intervals

负幂次对数加权的Trudinger-Moser不等式

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

应用数学 2024年第1期37卷 73-79页

作者：朱茂春马盼江苏大学数学科学学院江苏镇江212013

本文研究具有负幂次对数加权的Trudinger-Moser不等式.通过建立了一个径向引理,利用著名的Leckband泛函不等式证明了Calanchi和Ruf(2015)得到的对数加权Trudinger-Moser不等式在负幂次情形依然成立.

关键词：径向负幂次对数加权 Trudinger-Moser不等式

全空间上与Trudinger-Moser-Lorentz不等式相关的集中紧性原理

在线全文

学校读者我要写书评

暂无评论

应用数学学报 2021年第2期44卷 294-306页

作者：朱茂春李栋梁江苏大学数学科学学院江苏大学应用系统分析研究院镇江212013

本文研究了全空间上与Trudinger-Moser-Lorentz不等式相关的集中紧性原理.利用函数的水平截断方法,我们将有界区域上与Trudinger-Moser-Lorentz不等式相关的集中紧性原理推广到了无界区域上.此外,我们还构造了试验函数验证了结论的最佳性.

关键词： Trudinger-Moser不等式 Lorentz空间最佳常数重排集中紧性原理

二维空间上对数加权各向异性范数约束下的Trudinger-Moser不等式

在线全文

学校读者我要写书评

暂无评论

应用数学 2022年第4期35卷 766-775页

作者：朱茂春陈文欢江苏大学数学科学学院江苏镇江212013

本文研究二维空间上一类各向异性对数加权径向Sobolev空间上的Trudinger-Moser不等式.通过建立一个重要的径向引理,并利用著名的Leckband泛函不等式得到了对数加权约束下的最佳Trudinger-Moser增长指标,特别地,我们得到在极限情形β=1下... 详细信息

本文研究二维空间上一类各向异性对数加权径向Sobolev空间上的Trudinger-Moser不等式.通过建立一个重要的径向引理,并利用著名的Leckband泛函不等式得到了对数加权约束下的最佳Trudinger-Moser增长指标,特别地,我们得到在极限情形β=1下,Trudinger-Moser最佳增长为双指数形式增长.通过构造合适的测试函数序列证明了对数加权的Trudinger-Moser不等式中常数的最佳性.

关键词：各向异性径向对数加权 Trudinger-Moser不等式

通过多孔介质的二维磁流体力学方程组的全局正则性

在线全文

学校读者我要写书评

暂无评论

应用数学学报 2015年第1期38卷 8-15页

作者： S.Rahman 朱茂春西北工业大学应用数学系西安710129 南方信息科技学院北京师范大学数学科学学院北京100875

本文的目的是研究以不断吹/吸方式通过孔道流体的二维磁流体动力学方程(MHD)弱解的全局正则性.为此,我们将利用抛物正则化过程和在流动模型中流体的的Darcy定律.

关键词：弱解多孔介质二维磁流体力学方程组不可压缩粘弹性流体

在线全文

学校读者我要写书评

暂无评论

一体式活塞内模结构设计及应用

特种铸造及有色合金 2011年第7期31卷 634-635页

作者：何德生易绿林朱茂春张松中国长安汽车集团湖南江滨活塞分公司

采用一体式内模代替原来的两体式内模铸造模具,简化了模具制造工艺、节约了制造成本、美化了活塞内腔。利用Magma软件模拟浇注,发现一体式内模容易出现的缺陷以及缺陷存在的位置,并提出有效的解决方法。通过在小缸径活塞上的实际应用,... 详细信息

采用一体式内模代替原来的两体式内模铸造模具,简化了模具制造工艺、节约了制造成本、美化了活塞内腔。利用Magma软件模拟浇注,发现一体式内模容易出现的缺陷以及缺陷存在的位置,并提出有效的解决方法。通过在小缸径活塞上的实际应用,取得了良好的效果。

关键词：整体内模一体式两体式排气销冷却参数

New insight into the origin and evolution of the flora and fauna of Hainan Island, China

在线全文

学校读者我要写书评

暂无评论

Science China Earth Sciences 2025年第1期68卷 52-61页

作者： Hua zhu Center for Integrative Conservation Xishuangbanna Tropical Botanical Garden Chinese Academy of Sciences Yunnan International Joint Laboratory of Southeast Asia Biodiversity Conservation Yunnan Key Laboratory for the Conservation of Tropical Rainforests and Asian Elephants

The origin of the biota of Hainan Island, China, remains a fundamental scientific problem. Comparative studies on the biota, geological tectonics, and paleomagnetism proposed that during the Eocene, Hainan Island connected Vietnam and Guangxi, and then moved to the southeast to reach its present location. This review mainly discusses its biota origin from molecular phylogeny and palaeobotanical research. The formation and evolution of the biological groups of Hainan Island were identified via research on their genomes, phylogeny, and molecular biogeography. This research showed that the genera and species that appeared and diverged early in their evolution(i.e., before the Miocene) can be explained by the land connection between Hainan Island, Vietnam, and Guangxi during the Eocene-Oligocene. According to Southeast Asian tectonic theory, in the Middle Miocene(at about 15 million years ago), Hainan Island had moved to its present position. The population and genetic divergence of species with late divergence times(after 15 Ma) can be reasonably explained by the close proximity(or land connection) between Hainan Island and the Leizhou Peninsula, enabling genetic communication between Hainan Island and the Chinese mainland, but have exceptional cases. Conclusions have been obtained through palaeobotanical studies, showing that in the Eocene-Oligocene period, southwest China and Hainan Island had subtropical vegetation and flora. However, the fossil group in southeast China(in Maoming, near present-day Hainan Island) in the Late Eocene indicated a tropical rainforest vegetation and flora. This suggests that in the Paleogene, Hainan Island may have been located near or on the southwest border of Guangxi and northern Vietnam, rather than in its present location. The floristic division of the flora of Hainan Island basically presents a northeast-southwest inclined distribution pattern. This pattern can be explained by the counterclockwise rotation of Hainan Island during i

关键词： Molecular phylogeny Biogeography Paleobotany Origin of flora and fauna Hainan Island of China

同方期刊数据库

Modification of Maxwell model for conductivity prediction of carbon nanotubes-filled polymer composites with tunneling effect

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2025年第1期46卷 25-36页

作者： Jue zhu Longyuan LI Ningtao zhu Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline Key Laboratory of Impact and Safety Engineering (Ningbo University) Ministry of Education School of Engineering Computing and Mathematics University of Plymouth Xi'an Zhanshi Testing & Engineering Co.Ltd.

Carbon nanotubes(CNTs) have garnered great attention in recent years due to their outstanding electrical, thermal, and mechanical properties. The incorporation of small amounts of CNTs in polymers can substantially improve the sensitivity of the polymer's electrical conductivity. This paper presents a modified Maxwell model to evaluate the electrical conductivity of CNTs-filled polymer composites by introducing a transition zone to account for the tunneling effect. In this modified Maxwell model, the CNTs-filled polymer composite is modeled as a three-phase composite, consisting of a matrix(polymer), inclusions(CNTs), and a transition zone(tunneling zone). The effective electrical conductivity(EEC) of the composite is calculated based on the volume fractions and electrical conductivities of the matrix, inclusions, and transition zone. The model's validity is confirmed through the use of available test data, which demonstrates its capability to accurately capture the nonlinear conductivity behavior observed in CNTs-polymer composites. This study offers valuable insights into the design of high-performance conductive polymer nanocomposites, and enhances the understanding of electrical conduction mechanisms in CNT-dispersed polymer composites.

关键词： Nanoclay