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Zeitschrift für angewandte Mathematik und Physik最新文献

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Novel description for optimality principle of cerebral arteries within the circle of Willis: a Womersley number-based scaling law 威利斯圈内脑动脉优化原理的新描述：基于沃默斯利数的缩放定律
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-23 DOI: 10.1007/s00033-024-02257-0
Mohammad Shumal, Mohsen Saghafian, Ebrahim Shirani, Mahdi Nili-Ahmadabadi
{"title":"Novel description for optimality principle of cerebral arteries within the circle of Willis: a Womersley number-based scaling law","authors":"Mohammad Shumal, Mohsen Saghafian, Ebrahim Shirani, Mahdi Nili-Ahmadabadi","doi":"10.1007/s00033-024-02257-0","DOIUrl":"https://doi.org/10.1007/s00033-024-02257-0","url":null,"abstract":"","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141105275","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
On the well-posedness of the Cauchy problem for the two-component peakon system in $$C^kcap W^{k,1}$$ 关于 $$C^kcap W^{k,1}$$ 中两分量峰子系统的考奇问题的良好提出性
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-15 DOI: 10.1007/s00033-024-02246-3
K. H. Karlsen, Ya. Rybalko
{"title":"On the well-posedness of the Cauchy problem for the two-component peakon system in $$C^kcap W^{k,1}$$","authors":"K. H. Karlsen, Ya. Rybalko","doi":"10.1007/s00033-024-02246-3","DOIUrl":"https://doi.org/10.1007/s00033-024-02246-3","url":null,"abstract":"<p>This study focuses on the Cauchy problem associated with the two-component peakon system featuring a cubic nonlinearity, constrained to the class <span>((m,n)in C^{k}(mathbb {R}) cap W^{k,1}(mathbb {R}))</span> with <span>(kin mathbb {N}cup {0})</span>. This system extends the celebrated Fokas–Olver–Rosenau–Qiao equation and the following nonlocal (two-place) counterpart proposed by Lou and Qiao: </p><span>$$begin{aligned} partial _t m(t,x)= partial _x[m(t,x)(u(t,x)-partial _xu(t,x)) (u(-t,-x)+partial _x(u(-t,-x)))], end{aligned}$$</span><p>where <span>(m(t,x)=left( 1-partial _{x}^2right) u(t,x))</span>. Employing an approach based on Lagrangian coordinates, we establish the local existence, uniqueness, and Lipschitz continuity of the data-to-solution map in the class <span>(C^kcap W^{k,1})</span>. Moreover, we derive criteria for blow-up of the local solution in this class.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940265","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
On multiplicity and concentration for a magnetic Kirchhoff–Schrödinger equation involving critical exponents in $$mathbb {R}^{2}$$ 论涉及 $$mathbb {R}^{2}$ 中临界指数的基尔霍夫-薛定谔磁性方程的多重性和集中性
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-15 DOI: 10.1007/s00033-024-02260-5
Xiaolu Lin, Shenzhou Zheng
{"title":"On multiplicity and concentration for a magnetic Kirchhoff–Schrödinger equation involving critical exponents in $$mathbb {R}^{2}$$","authors":"Xiaolu Lin, Shenzhou Zheng","doi":"10.1007/s00033-024-02260-5","DOIUrl":"https://doi.org/10.1007/s00033-024-02260-5","url":null,"abstract":"<p>In this paper, we prove the multiplicity and concentration behavior of complex-valued solutions for the following Kirchhoff–Schrödinger equation with magnetic field </p><span>$$begin{aligned} -bigg (avarepsilon ^2+bvarepsilon [u]^2_{A/varepsilon }bigg )Delta _{A/varepsilon } u+V(x)u=f(|u|^2)u,quad xin mathbb {R}^{2}, end{aligned}$$</span><p>where <span>(varepsilon &gt;0)</span> is a small parameter, the nonlinearity <i>f</i> is involved in critical exponential growth in the sense of Trudinger–Moser inequality and both <span>(V:mathbb {R}^{2}rightarrow mathbb {R})</span> and <span>(A:mathbb {R}^{2}rightarrow mathbb {R}^{2})</span> are continuous potential and magnetic potential, respectively. Imposing a local constraint of potential <i>V</i>(<i>x</i>) first introduced from del Pino and Felmer, we get the multiplicity of solutions by way of the relationship between the number of the solutions and the topology of the set with <i>V</i> attaining the minimum. Our strategy of main proof is based on the variational methods combined with the penalization technique, the Trudinger–Moser inequality and Ljusternik–Schnirelmann theory, and our result is still new even without magnetic effect.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940334","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
Convergence rate for a regularized scalar conservation law 正则化标量守恒定律的收敛率
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-15 DOI: 10.1007/s00033-024-02259-y
Billel Guelmame, Haroune Houamed
{"title":"Convergence rate for a regularized scalar conservation law","authors":"Billel Guelmame, Haroune Houamed","doi":"10.1007/s00033-024-02259-y","DOIUrl":"https://doi.org/10.1007/s00033-024-02259-y","url":null,"abstract":"<p>This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the Lebesgue spaces <span>(L^infty _{textrm{loc}}(mathbb {R}^+;L^p(mathbb {R})))</span>, for any <span>(p in [1,infty ))</span>, as the regularization parameter <span>(ell )</span> approaches zero. Notably, we demonstrate that this stability result is accompanied by a quantifiable rate of convergence. A key insight in our proof lies in the observation that the fluctuations of the solutions remain under control in low regularity spaces, allowing for a potential quantification of their behavior in the limit as <span>(ell rightarrow 0)</span>. This is achieved through a careful asymptotic analysis of the perturbative terms in the regularized equation, which, in our view, constitutes a pivotal contribution to the core findings of this paper.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940340","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
Dynamics of the prey–predator model with variable coefficients and degenerate diffusion coefficients 具有可变系数和退化扩散系数的捕食者-捕食者模型的动力学特性
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-15 DOI: 10.1007/s00033-024-02258-z
Guoying Yang, Shaowen Yao
{"title":"Dynamics of the prey–predator model with variable coefficients and degenerate diffusion coefficients","authors":"Guoying Yang, Shaowen Yao","doi":"10.1007/s00033-024-02258-z","DOIUrl":"https://doi.org/10.1007/s00033-024-02258-z","url":null,"abstract":"<p>The long-time behaviors are an important topic in the study of reaction diffusion equations. It is of interest to understand effects of variable coefficients and degenerate diffusion coefficients on the dynamical properties of reaction diffusion equations. In this paper, we shall use some new methods and techniques to prove that the degradation of the diffusion coefficient of the prey and variable coefficients satisfying the appropriate conditions will not affect dynamical properties of the reaction–diffusion prey–predator model.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940159","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
Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model 非线性增长、交叉扩散和保护区对扩散捕食模型的影响
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-11 DOI: 10.1007/s00033-024-02254-3
Daoxin Qiu, Yunfeng Jia, Jingjing Wang
{"title":"Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model","authors":"Daoxin Qiu, Yunfeng Jia, Jingjing Wang","doi":"10.1007/s00033-024-02254-3","DOIUrl":"https://doi.org/10.1007/s00033-024-02254-3","url":null,"abstract":"<p>This paper concerns a diffusive predation model with nonlinear growth, cross-diffusion and protection zone terms. The main purpose is to investigate the effects of nonlinear growth and cross-diffusion on the coexistent solution when protection zone is present. Firstly, a priori estimate and the existence of positive solutions are discussed, including local and global existence. Then, some asymptotic properties of coexistent solutions induced by the mortality rate, nonlinear growth of predator and cross-diffusion are analyzed. It is revealed that there exist critical values related to certain principal eigenvalues such that the nonlinear growth, cross-diffusion and protection zone all have significant effects on the coexistent solutions; as far as the nonlinear growth concerned, we find that it has important influences on the coexistence region of two species undoubtedly. Biologically, this implies that these critical values greatly affect the survival of species.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940329","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 effect of self-memory-based diffusion on a predator–prey model 基于自我记忆的扩散对捕食者-猎物模型的影响
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-10 DOI: 10.1007/s00033-024-02256-1
Yunzhuo Zhang, Xuebing Zhang, Shunjie Li
{"title":"The effect of self-memory-based diffusion on a predator–prey model","authors":"Yunzhuo Zhang, Xuebing Zhang, Shunjie Li","doi":"10.1007/s00033-024-02256-1","DOIUrl":"https://doi.org/10.1007/s00033-024-02256-1","url":null,"abstract":"<p>In this research, we examine a diffusive predator–prey model with spatial memory. We begin by checking that the suggested model has a unique solution that is boundedness. The stability of each equilibrium is then examined. Local and global stability as well as bifurcations are investigated in the non-delayed model at stationary equilibrium. Then, we investigate the Hopf bifurcation using the delay as the bifurcation parameter. In order to back up our theoretical findings, we then give some numerical simulations.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942407","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
Lamb waves in stratified plates: appearance of “forbidden” phase velocities 分层板块中的λ波："禁止 "相速度的出现
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-09 DOI: 10.1007/s00033-024-02245-4
Sergey V. Kuznetsov
{"title":"Lamb waves in stratified plates: appearance of “forbidden” phase velocities","authors":"Sergey V. Kuznetsov","doi":"10.1007/s00033-024-02245-4","DOIUrl":"https://doi.org/10.1007/s00033-024-02245-4","url":null,"abstract":"<p>It is known that Lamb waves in homogeneous traction-free plates can propagate with arbitrary phase velocity, spanning the admissible speed interval (0;<span>(+infty ))</span>. However, as the current research shows, Lamb waves propagating in two-layered traction-free plates may have ‘forbidden’ phase velocities, at which no Lamb waves can propagate. The analysis is based on the approach comprising Cauchy complex formalism and the exponential fundamental matrix method.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940137","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
Global dynamics of a Lotka-Volterra competition-diffusion system with advection and nonlinear boundary conditions 具有平流和非线性边界条件的 Lotka-Volterra 竞争-扩散系统的全局动力学
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-07 DOI: 10.1007/s00033-024-02249-0
Chenyuan Tian, Shangjiang Guo
{"title":"Global dynamics of a Lotka-Volterra competition-diffusion system with advection and nonlinear boundary conditions","authors":"Chenyuan Tian, Shangjiang Guo","doi":"10.1007/s00033-024-02249-0","DOIUrl":"https://doi.org/10.1007/s00033-024-02249-0","url":null,"abstract":"<p>In this paper, we deal with the global dynamics of a Lotka-Volterra competition-diffusion-advection system with nonlinear boundary conditions, including the existence, nonexistence and global stability of coexistence steady states. We start with the investigation of the principal eigenvalue of linearized system to get the local stability of steady states and then discuss the global dynamics in terms of competition coefficients.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940335","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
Vorticity Leray- $$alpha $$ model for Navier–Stokes equations with viscosity depending on the distance to the wall 纳维-斯托克斯方程的旋涡勒雷- $$alpha $$ 模型，粘度取决于到墙壁的距离
Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-07 DOI: 10.1007/s00033-024-02252-5
Guillaume Leloup
{"title":"Vorticity Leray- $$alpha $$ model for Navier–Stokes equations with viscosity depending on the distance to the wall","authors":"Guillaume Leloup","doi":"10.1007/s00033-024-02252-5","DOIUrl":"https://doi.org/10.1007/s00033-024-02252-5","url":null,"abstract":"<p>We introduce a vorticity Leray-<span>(alpha )</span> model with eddy viscosity depending on <span>(d(x,partial Omega )^eta )</span> where <span>(partial Omega )</span> is the boundary of the domain and <span>(eta in ]0;1[)</span>. We prove that this system admits fairly regular weak solutions converging when <span>(alpha )</span> goes to 0 to the solution of a reference system</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942532","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
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