Zeitschrift für angewandte Mathematik und Physik最新文献_第4页

Interactions of stationary wave with rarefaction wave and shock wave for a blood flow model in arteries 动脉血流模型中静止波与稀释波和冲击波的相互作用

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-30 DOI: 10.1007/s00033-024-02295-8

Wancheng Sheng, Shufang Xu

引用次数: 0

Existence and concentration behavior of normalized solutions for critical Kirchhoff type equations with general nonlinearities 具有一般非线性的临界基尔霍夫型方程的归一化解的存在性和集中行为

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-29 DOI: 10.1007/s00033-023-02178-4

Shuyao Lu, Anmin Mao

{"title":"Existence and concentration behavior of normalized solutions for critical Kirchhoff type equations with general nonlinearities","authors":"Shuyao Lu, Anmin Mao","doi":"10.1007/s00033-023-02178-4","DOIUrl":"https://doi.org/10.1007/s00033-023-02178-4","url":null,"abstract":"We consider the following Kirchhoff equation in the Sobolev critical case with combined power nonlinearities having prescribed mass $$begin{aligned} mathop {int }limits _{{mathbb {R}}^{3}}|u|^2 =c^2, end{aligned}$$where (a, c, mu >0) are positive constants, (b>0) is a positive parameter, (2<q<{bar{p}}:=2+frac{8}{3}) which is (L^{2})-critical exponent. For the (L^{2})-subcritical case (2<q<frac{10}{3}) and Sobolev critical case, Li et al. (2021) proved that (({mathcal {K}})) has a solution which is ground state solution and corresponds to local minima of the associated energy functional. Here we extend the result in Li et al. (2021) by proving that (({mathcal {K}})) has the second solution which is not a ground state and is located at a mountain-pass level of the energy functional. Meanwhile, let (u_{b}) are normalized solutions of mountain-pass type to (({mathcal {K}})), then (u_{b}rightarrow u) in (H^{1}({mathbb {R}}^{3})) as (brightarrow 0) up to a subsequence, where (uin H^{1}({mathbb {R}}^{3})) is a normalized solution of mountain-pass type to $$begin{aligned} -atriangle u =lambda u+ mu |u|^{q-2}u +|u|^{4}u textrm{in} {{mathbb {R}}^{3}}. end{aligned}$$Our results also extend the results of Soave (J Differ Equ 269:6941–6987, 2020; J Funct Anal 279:108610, 2020).","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Vectfem: a generalized MATLAB-based vectorized algorithm for the computation of global matrix/force for finite elements of any type and approximation order in linear elasticity Vectfem：基于 MATLAB 的通用矢量化算法，用于计算线性弹性中任何类型和近似阶次的有限元的全局矩阵/力

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-28 DOI: 10.1007/s00033-024-02293-w

Baurice Sylvain Sadjiep Tchuigwa, Jan Krmela, Jan Pokorny, Vladimíra Krmelová, Petr Jilek

{"title":"Vectfem: a generalized MATLAB-based vectorized algorithm for the computation of global matrix/force for finite elements of any type and approximation order in linear elasticity","authors":"Baurice Sylvain Sadjiep Tchuigwa, Jan Krmela, Jan Pokorny, Vladimíra Krmelová, Petr Jilek","doi":"10.1007/s00033-024-02293-w","DOIUrl":"https://doi.org/10.1007/s00033-024-02293-w","url":null,"abstract":"In this paper, we introduce a new vectorized MATLAB-based algorithm for efficient serial computation of global matrix/force arising from finite element method (FEM) for meshes of any type and approximation order in linear elasticity. Because for-loops in MATLAB are very slow, we propose a modified process that takes advantage of vectorization and sparse assembly to achieve good performance while using the same memory as the standard algorithm. For this purpose, by using good programming practices, the implementation of this scheme is succinctly described and can be integrated into any MATLAB package dealing with FEM. Specifically, attention is paid to the calculation of the triplet (row index, column index, matrix components) as well as the assembly of the global stiffness matrix, mass matrix and force vector. Additionally, an extension of the proposed approach for Mindlin plate theory and functionally graded materials is outlined. Finally, the accuracy of this strategy is verified on selected numerical tests after comparing the obtained results with those of ABAQUS. In terms of performance, the study conducted on a set of meshes considering the standard algorithm and two other well-known MATLAB vectorized algorithms revealed that: (i) for a 2D beam problem meshed with (P_{1})-triangle elements, a speedup of about 8 and 15 is achieved with sparse and fsparse, respectively. (ii) for a 3D plate problem meshed with (P_{1})-tetrahedral elements, a speedup of about 4 and 8 is achieved with sparse and fsparse, respectively. When compared to ABAQUS performance, the proposed scheme results in a computational time that is about five times smaller.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strain-induced ultrafast magnetization dynamics in cubic magnetostrictive materials with inertial and nonlinear dissipative effects 具有惯性和非线性耗散效应的立方磁致伸缩材料中的应变诱导超快磁化动力学

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-28 DOI: 10.1007/s00033-024-02289-6

Sarabindu Dolui, Sumit Maity, Sharad Dwivedi

引用次数: 0

A strong form of propagation of chaos for Cucker–Smale model 卡克-斯马尔模型的强混沌传播形式

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-28 DOI: 10.1007/s00033-024-02291-y

Juntao Wu, Xiao Wang, Yicheng Liu

引用次数: 0

Critical blow-up exponent for a doubly dispersive quasilinear wave equation 双分散准线性波方程的临界炸毁指数

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-28 DOI: 10.1007/s00033-024-02296-7

Bingchen Liu, Mengyao Liu

引用次数: 0

Concentration of solutions for non-autonomous double-phase problems with lack of compactness 缺乏紧凑性的非自治双相问题的集中解法

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-20 DOI: 10.1007/s00033-024-02290-z

Weiqiang Zhang, Jiabin Zuo, Vicenţiu D. Rădulescu

{"title":"Concentration of solutions for non-autonomous double-phase problems with lack of compactness","authors":"Weiqiang Zhang, Jiabin Zuo, Vicenţiu D. Rădulescu","doi":"10.1007/s00033-024-02290-z","DOIUrl":"https://doi.org/10.1007/s00033-024-02290-z","url":null,"abstract":"The present paper is devoted to the study of the following double-phase equation $$begin{aligned} -text {div}(|nabla u|^{p-2}nabla u+mu _{varepsilon }(x)|nabla u|^{q-2}nabla u)+V_{varepsilon }(x)(|u|^{p-2}u+mu _{varepsilon }(x)|u|^{q-2}u)=f(u)quad text{ in }quad mathbb {R}^{N}, end{aligned}$$where (Nge 2), (1<p<q<N), (q<p^{*}) with (p^{*}=frac{Np}{N-p}), (mu :mathbb {R}^{N}rightarrow mathbb {R}) is a continuous non-negative function, (mu _{varepsilon }(x)=mu (varepsilon x)), (V:mathbb {R}^{N}rightarrow mathbb {R}) is a positive potential satisfying a local minimum condition, (V_{{{,mathrm{varepsilon },}}}(x)=V({{,mathrm{varepsilon },}}x)), and the nonlinearity (f:mathbb {R}rightarrow mathbb {R}) is a continuous function with subcritical growth. Under natural assumptions on (mu ), V and f, by using penalization methods and Lusternik–Schnirelmann theory we first establish the multiplicity of solutions, and then, we obtain concentration properties of solutions.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Continuous data assimilation for the three-dimensional planetary geostrophic equations of large-scale ocean circulation 大尺度海洋环流三维行星地转方程的连续数据同化

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-18 DOI: 10.1007/s00033-024-02286-9

Bo You

引用次数: 0

Optimal scenario for road evacuation in an urban environment 城市环境中道路疏散的最佳方案

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-16 DOI: 10.1007/s00033-024-02278-9

Mickael Bestard, Emmanuel Franck, Laurent Navoret, Yannick Privat

{"title":"Optimal scenario for road evacuation in an urban environment","authors":"Mickael Bestard, Emmanuel Franck, Laurent Navoret, Yannick Privat","doi":"10.1007/s00033-024-02278-9","DOIUrl":"https://doi.org/10.1007/s00033-024-02278-9","url":null,"abstract":"How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem. We consider a macroscopic road traffic model on networks, semi-discretized in space and decide to give ourselves the possibility to control the flow at junctions. Our target is to smooth the traffic along a given path within a fixed time. A parsimony constraint is imposed on the controls, in order to ensure that the optimal strategies are feasible in practice. We perform an analysis of the resulting optimal control problem, proving the existence of an optimal control and deriving optimality conditions, which we rewrite as a single functional equation. We then use this formulation to derive a new mixed algorithm interpreting it as a mix between two methods: a descent method combined with a fixed point method allowing global perturbations. We verify with numerical experiments the efficiency of this method on examples of graphs, first simple, then more complex. We highlight the efficiency of our approach by comparing it to standard methods. We propose an open source code implementing this approach in the Julia language.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Minkowski dimension of suitable weak solutions of the 3D co-rotational Beris-Edwards system 三维同向旋转贝里斯-爱德华兹系统合适弱解的闵科夫斯基维度

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-07-14 DOI: 10.1007/s00033-024-02284-x

Zhongbao Zuo

引用次数: 0