Studies in Applied Mathematics最新文献

{"title":"Qualitative Analysis for a Fourth-Order Wave Equation With Exponential-Type Nonlinearity","authors":"Yunlong Gao, Chunyou Sun, Kaibin Zhang","doi":"10.1111/sapm.70034","DOIUrl":"https://doi.org/10.1111/sapm.70034","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with the properties of solutions to the following fourth-order wave equation with exponential-type nonlinearity:\u0000\u0000 </p><div><span><!--FIGURE--><span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>u</mi>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mi>Δ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mi>u</mi>\u0000 <mo>+</mo>\u0000 <mi>u</mi>\u0000 <mo>+</mo>\u0000 <mi>ω</mi>\u0000 <msup>\u0000 <mi>Δ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <msub>\u0000 <mi>u</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>μ</mi>\u0000 <msub>\u0000 <mi>u</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <annotation>$$begin{equation*} {u_{tt}} + {Delta ^2}u + u + omega {Delta ^2}{u_t} + mu {u_t} = f(u), end{equation*}$$</annotation>\u0000 </semantics></math></span><span></span></div>where the exponential nonlinearity <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is classified as either subcritical growth or critical growth at infinity, based on the Adams-type inequality. By utilizing the potential well theory and Adams-type inequality, we first prove the existence, stability, and blow-up of solutions at critical energy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>t</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$E(t_0)=d$</annotation>\u0000 </semantics></math>. Subsequently, when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 <mo>></mo>\u0000 <mo>−</mo>\u0000 <mi>ω</mi>\u0000 <msub>\u0000","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595047","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}

{"title":"Modeling Mosquito Population Suppression Using Beverton–Holt Offspring Survival Probability","authors":"Yining Chen,&nbsp;Yufeng Wang,&nbsp;Jianshe Yu,&nbsp;Jia Li","doi":"10.1111/sapm.70038","DOIUrl":"https://doi.org/10.1111/sapm.70038","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we develop a mathematical model for mosquito population suppression based on a Beverton–Holt type of offspring survival probability. We focus on the scenarios where sterile mosquitoes are released impulsively and periodically under the condition that the release period <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> is either equal to or greater than the sexually active lifespan <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>T</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>$overline{T}$</annotation>\u0000 </semantics></math> of the sterile mosquitoes. For the case where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>=</mo>\u0000 <mover>\u0000 <mi>T</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$T=overline{T}$</annotation>\u0000 </semantics></math>, we rigorously analyze the existence and stability of equilibrium states. When <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>&gt;</mo>\u0000 <mover>\u0000 <mi>T</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$T&gt;overline{T}$</annotation>\u0000 </semantics></math>, the model transforms into two switching equations. Our analysis demonstrates that in the absence of periodic solutions, the origin is globally asymptotically stable, whereas when a unique periodic solution exists, it is either globally asymptotically stable or semistable. In the scenarios where two periodic solutions emerge, one is stable and the other is unstable. Numerical simulations further illustrate the periodic dynamics of the model.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595049","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}

{"title":"The Maximal Lyapunov Exponent of a Stochastic Bautin Bifurcation System","authors":"Diandian Tang,&nbsp;Jingli Ren","doi":"10.1111/sapm.70035","DOIUrl":"https://doi.org/10.1111/sapm.70035","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the maximal Lyapunov exponent of a Bautin bifurcation system with additive white noise, which is also the fifth-order truncated normal form of a generalized Hopf bifurcation in the absence of noise. By solving the stationary density associated with the invariant measure of the system and its marginal distribution, we show that the maximal Lyapunov exponent is of indefinite sign depending on parameters and we give the explicit condition to control the range of the maximal Lyapunov exponent. Finally, we give the asymptotic expansion of the maximal Lyapunov exponent in the small noise limit.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564866","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}

{"title":"Matrix-Valued Cauchy Bi-Orthogonal Polynomials and a Novel Noncommutative Integrable Lattice","authors":"Shi-Hao Li,&nbsp;Ying Shi,&nbsp;Guo-Fu Yu,&nbsp;Jun-Xiao Zhao","doi":"10.1111/sapm.70040","DOIUrl":"https://doi.org/10.1111/sapm.70040","url":null,"abstract":"<div>\u0000 \u0000 <p>Matrix-valued Cauchy bi-orthogonal polynomials are proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in the four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non-abelian variables.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564742","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}

{"title":"Pullback Attractors for Nonclassical Diffusion Equations With a Delay Operator","authors":"Bin Yang,&nbsp;Yuming Qin,&nbsp;Alain Miranville,&nbsp;Ke Wang","doi":"10.1111/sapm.70039","DOIUrl":"https://doi.org/10.1111/sapm.70039","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we consider the asymptotic behavior of weak solutions for nonclassical nonautonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;annotation&gt;$g$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfies subcritical exponent growth conditions, the delay operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$varphi (t, u_t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; contains some hereditary characteristics, and the external force &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k in L_{l o c}^{2}left(mathbb {R}; L^{2}(Omega)right)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. First, we prove the well-posedness of solutions by using the Faedo–Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time-dependent spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$C_{mathcal {H}_{t}(Omega)}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554571","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}

{"title":"David J. Kaup and Boson Stars","authors":"Stoytcho Yazadjiev","doi":"10.1111/sapm.70041","DOIUrl":"https://doi.org/10.1111/sapm.70041","url":null,"abstract":"<div>\u0000 \u0000 <p>David Kaup's 1968 paper, “Klein–Gordon Geon”, introduced one of the first detailed studies of self-gravitating configurations of a complex scalar field, known as boson stars. These objects, formed by a massive complex scalar field interacting with gravity, provide a compelling theoretical model for understanding various phenomena in astrophysics and cosmology, particularly in the context of dark matter. Kaup's pioneering work, which considered the Einstein–Klein–Gordon equations, remains foundational in the study of nontopological solitons and self-gravitating systems in general.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143555018","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}

{"title":"Mathematical Modeling and Analysis of Atherosclerosis Based on Fluid-Multilayered Poroelastic Structure Interaction Model","authors":"Yanning An,&nbsp;Wenjun Liu","doi":"10.1111/sapm.70028","DOIUrl":"https://doi.org/10.1111/sapm.70028","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we establish a model of atherosclerosis in the early stage based on fluid-structure interaction (FSI) model of blood vessel and prove the existence of weak solutions. The model consists of Navier–Stokes equation, Biot equations, and reaction–diffusion equations, which involves the effect of blood flow velocity on the concentration of low-density lipoprotein (LDL) and other biological components. We first divide the model into an FSI submodel and a coupled reaction–diffusion submodel, respectively. Then, by using Rothe's method and operator splitting numerical scheme, we obtain the existence of weak solution of FSI submodel. In order to solve the nonlinear term representing the consumption of oxidized low-density lipoprotein (oxLDL), we construct a regular system. The results in FSI submodel together with Schauder's fixed-point theorem allow us to obtain the existence of nonnegative weak solutions for the reaction–diffusion submodel by showing the existence and nonnegativity of weak solutions for the regular system. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify that vascular narrowing caused by plaque further exacerbates plaque growth.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533497","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}

{"title":"Weak Solutions and Simulations for a Generalized Phase-Field Crystal Model With Neumann Boundary Conditions","authors":"Guomei Zhao,&nbsp;Fan Wu,&nbsp;Peicheng Zhu","doi":"10.1111/sapm.70031","DOIUrl":"https://doi.org/10.1111/sapm.70031","url":null,"abstract":"<div>\u0000 \u0000 <p>We study a generalized phase-field crystal (GPFC) model, which is a quasilinear parabolic equation of sixth-order for an order parameter. The model is used to simulate the microstructure evolution in crystal growth, specifically focusing on the competition between square, hexagonal, and roll forms. Here, the global existence and uniqueness of weak solutions in three space dimensions are proved under Neumann boundary conditions by employing the Galerkin method. The rigorous connection between weak solutions to the PFC and the GPFC equations is established through an analysis of the asymptotic limit. Moreover, we carry out numerical simulations to validate the model.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521870","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}

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70032","DOIUrl":"https://doi.org/10.1111/sapm.70032","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513583","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}

{"title":"Dynamics Analysis for Diffusive Resource-Consumer Model With Nonlocal Discrete Memory","authors":"Haihui Wu,&nbsp;Xiaoqin Shen,&nbsp;Aili Wang,&nbsp;Qian Li","doi":"10.1111/sapm.70030","DOIUrl":"https://doi.org/10.1111/sapm.70030","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, based on the importance of consumer memory on spatial resource distribution, we propose a novel consumer-resource model that incorporates nonlocal discrete memory. By conducting thorough bifurcation and stability analysis, we determine the conditions for the occurrence of Hopf and Turing bifurcations and reveal a unique dynamic phenomenon termed Turing–Hopf bifurcation, which is uncommon in models without nonlocal discrete memory. We also show that as the memory delay increases, both the spatially nonhomogeneous periodic and steady-state solutions may vanish, and the unstable positive homogeneous steady state may regain stability. Furthermore, leveraging the theory of normal forms, we derive a new effective algorithm to determine the direction and stability of Hopf bifurcation in a model where the diffusion component incorporates an integral term with delay. In addition, we perform numerical simulations to validate our theoretical findings, particularly to assess the direction and stability of the delay-induced mode-1 Hopf bifurcation. Our new method is used for this purpose, and the results have been confirmed by rigorous numerical analysis.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489706","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}