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Dynamics for a Diffusive Epidemic Model With a Free Boundary: Spreading Speed 具有自由边界的扩散性流行病模型的动力学：传播速度
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1111/sapm.12796
Xueping Li, Lei Li, Mingxin Wang
{"title":"Dynamics for a Diffusive Epidemic Model With a Free Boundary: Spreading Speed","authors":"Xueping Li,&nbsp;Lei Li,&nbsp;Mingxin Wang","doi":"10.1111/sapm.12796","DOIUrl":"https://doi.org/10.1111/sapm.12796","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the spreading speed of a diffusive epidemic model proposed by Li et al. [Dynamics for a diffusive epidemic model with a free boundary: spreading-vanishing dichotomy, Zeitschrift für Angewandte Mathematik und Physik 75 (2024): Article No. 202], where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading-vanishing dichotomy and some sharp criteria were obtained in Li et al. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(u,v)$</annotation>\u0000 </semantics></math>. Our arguments depend crucially on some detailed understandings for a corresponding semi-wave problem and a steady-state problem.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714673","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 the Equations of Compressible Fluid Dynamics With Cattaneo-Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure 关于热通量的卡塔尼奥式扩展的可压缩流体力学方程：对称性和松弛结构
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1111/sapm.12790
Felipe Angeles
{"title":"On the Equations of Compressible Fluid Dynamics With Cattaneo-Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure","authors":"Felipe Angeles","doi":"10.1111/sapm.12790","DOIUrl":"https://doi.org/10.1111/sapm.12790","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid dynamics with Cattaneo-type extensions for the heat flux. In contrast, the linearizations of such system around constant equilibrium solutions have Friedrichs symmetrizers. Then, from a physical perspective, we aim to understand the relaxation term appearing in this system. By noticing the violation of the Kawashima–Shizuta condition, locally and smoothly, with respect to the Fourier frequencies, we construct persistent waves, that is, solutions preserving the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^{2}$</annotation>\u0000 </semantics></math> norm for all times that are not dissipated by the relaxation terms.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142724193","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
A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction 以热传导引起的耗散为重点的可压缩流拉格朗日模型
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1111/sapm.12791
M. Scholle, S. Ismail-Sutton, P. H. Gaskell
{"title":"A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction","authors":"M. Scholle,&nbsp;S. Ismail-Sutton,&nbsp;P. H. Gaskell","doi":"10.1111/sapm.12791","DOIUrl":"https://doi.org/10.1111/sapm.12791","url":null,"abstract":"<p>With the aim of describing compressible viscous flows by means of a variational principle that takes into account heat conduction, a recently proposed Lagrangian is subjected to a detailed linear wave analysis that stems directly from the Lagrangian. The accompanying thermodynamic equation of state employed leads to a natural decomposition of the conduction term into three contributions, with the importance of each accessed through a detailed analysis employing a recently developed perturbation methodology giving rise to a favorable system of governing Jacobi equations. In addition to the model Lagrangian itself, three potential model scenarios—based on different combinations of the contributions forming the Lagrangian—are rigorously evaluated and appraised, regarding the occurrence, or otherwise, of dissipation recognizable by an attenuation of harmonic waves. Results reveal that two of the four models are suitable candidates, and suggest one in particular.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12791","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of a Nonlocal Dispersal Population Model With Annually Synchronized Emergence of Adults 成体每年同步出现的非本地散布种群模型的动态变化
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1111/sapm.12798
Zhenzhen Li, Binxiang Dai, Xingfu Zou
{"title":"Dynamics of a Nonlocal Dispersal Population Model With Annually Synchronized Emergence of Adults","authors":"Zhenzhen Li,&nbsp;Binxiang Dai,&nbsp;Xingfu Zou","doi":"10.1111/sapm.12798","DOIUrl":"https://doi.org/10.1111/sapm.12798","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is devoted to studying the spatial dynamics of a nonlocal dispersal species model with annually synchronized emergence of adults. In the situation of a bounded domain, we show threshold dynamics of the adult population, and provide exact persistence criterion. In the situation of a spatially homogeneous unbounded domain, we obtain the existence and computation formula of spreading speeds, which coincide with the minimal wave speed for the traveling waves. The above results are obtained in both monotone and nonmonotone cases of maturation impulse function. Numerical simulations are carried out to demonstrate the theoretical results.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714674","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 a Memory-Based Diffusion Model With Maturation Delay and Spatial Heterogeneity 具有成熟延迟和空间异质性的基于记忆的扩散模型的动力学原理
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1111/sapm.12793
Xiaohong Bu, Guohong Zhang, Yongli Song, Xiaoli Wang
{"title":"Dynamics of a Memory-Based Diffusion Model With Maturation Delay and Spatial Heterogeneity","authors":"Xiaohong Bu,&nbsp;Guohong Zhang,&nbsp;Yongli Song,&nbsp;Xiaoli Wang","doi":"10.1111/sapm.12793","DOIUrl":"https://doi.org/10.1111/sapm.12793","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider a single memory-based diffusion population model with maturation delay, spatial heterogeneity, and Neumann boundary condition. When the integral of the intrinsic growth rate over the domain is nonnegative, we obtain sufficient conditions for the local stability of the positive steady state and the critical values of maturation delay for the associated Hopf bifurcation. When the integral of the intrinsic growth rate over the domain is negative, considering that the characteristic equation involves a non-self-adjoint operator and two delays, we utilize a geometric method to determine all bifurcation points in terms of memory and maturation delays. The impact of spatial heterogeneity on the distribution of solutions is also examined via numerical simulations. It is found that the core area of high population density is coincident with the source area of growth rate. This suggests the importance of spatial heterogeneity in shaping the distribution and dynamics of the species.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714672","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
Issue Information-TOC 发行信息-TOC
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-26 DOI: 10.1111/sapm.12709
{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.12709","DOIUrl":"https://doi.org/10.1111/sapm.12709","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142724242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of Standing Periodic Waves in the Massive Thirring Model 大规模瑟林模型中驻留周期波的稳定性
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-26 DOI: 10.1111/sapm.12789
Shikun Cui, Dmitry E. Pelinovsky
{"title":"Stability of Standing Periodic Waves in the Massive Thirring Model","authors":"Shikun Cui,&nbsp;Dmitry E. Pelinovsky","doi":"10.1111/sapm.12789","DOIUrl":"https://doi.org/10.1111/sapm.12789","url":null,"abstract":"<p>We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum. We show analytically that each family of standing periodic waves is distinguished by the location of eight eigenvalues which coincide with the end points of the spectral bands of the Lax spectrum. The standing periodic waves are proven to be spectrally stable if the eight eigenvalues are located either on the imaginary axis or along the diagonals of the complex plane. By computing the Lax spectrum numerically, we show that this stability criterion is satisfied for some standing periodic waves.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12789","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142724225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation Dynamics in Time-Periodic Reaction–Diffusion Systems with Network Structures 具有网络结构的时间周期反应-扩散系统中的传播动力学
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-16 DOI: 10.1111/sapm.12788
Dong Deng, Wan-Tong Li, Shigui Ruan, Liang Zhang
{"title":"Propagation Dynamics in Time-Periodic Reaction–Diffusion Systems with Network Structures","authors":"Dong Deng,&nbsp;Wan-Tong Li,&nbsp;Shigui Ruan,&nbsp;Liang Zhang","doi":"10.1111/sapm.12788","DOIUrl":"https://doi.org/10.1111/sapm.12788","url":null,"abstract":"<div>\u0000 \u0000 <p>The main purpose of this paper is to study the propagation dynamics for a class of time-periodic reaction–diffusion systems with network structures. In the first part, by using the persistence theory, we obtain threshold results for the extinction and uniform persistence of the corresponding periodic ordinary differential system. The second part is concerned with the asymptotic speed of spread and traveling wave solutions. The uniform boundedness of solutions is proved by employing the refined high-dimensional local <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^{p}$</annotation>\u0000 </semantics></math>-estimate and abstract periodic evolution theories and the spreading properties of the corresponding solutions are established. We also prove the existence of the critical periodic traveling wave with wave speed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$c=c^{*}$</annotation>\u0000 </semantics></math> by using a delicate limitation argument. Finally, these results are applied to a multistage epidemiological model.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142724213","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
A Nonlocal Reaction-Diffusion-Advection System Modeling the Phytoplankton and Zooplankton 模拟浮游植物和浮游动物的非局部反应-扩散-对流系统
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-15 DOI: 10.1111/sapm.12785
Biao Wang, Hua Nie, Jianhua Wu
{"title":"A Nonlocal Reaction-Diffusion-Advection System Modeling the Phytoplankton and Zooplankton","authors":"Biao Wang,&nbsp;Hua Nie,&nbsp;Jianhua Wu","doi":"10.1111/sapm.12785","DOIUrl":"https://doi.org/10.1111/sapm.12785","url":null,"abstract":"<div>\u0000 \u0000 <p>We present a nonlocal reaction-diffusion-advection system that models the predator–prey relationship between zooplankton and phytoplankton species in a eutrophic vertical water column. The invasion dynamics of zooplankton are analyzed in terms of the spontaneous death rates and buoyant/sinking velocities of both phytoplankton and zooplankton. Our analysis reveals that the zooplankton species can successfully invade and coexist with the phytoplankton only under conditions of low spontaneous death rates and matching buoyant/sinking velocities with phytoplankton. Additionally, we derived asymptotic profiles for the unique positive steady state of this system when one of the sinking or buoyant velocities of either phytoplankton or zooplankton approaches infinity, while the other velocity remains fixed. These findings highlight the significant role of advection due to buoyancy in shaping the dynamics of plankton ecosystems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714681","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
Weakly Compressible Approximation of the Taylor–Green Vortex Solution 泰勒-格林涡旋解的弱可压缩近似值
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-11-15 DOI: 10.1111/sapm.12792
Matteo Antuono, Salvatore Marrone
{"title":"Weakly Compressible Approximation of the Taylor–Green Vortex Solution","authors":"Matteo Antuono,&nbsp;Salvatore Marrone","doi":"10.1111/sapm.12792","DOIUrl":"https://doi.org/10.1111/sapm.12792","url":null,"abstract":"<p>The Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math>. In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12792","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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