Studies in Applied Mathematics最新文献

{"title":"Bifurcation Near a Transcritical Singularity in Planar Singularly Perturbed Systems","authors":"Jianhe Shen,&nbsp;Xiang Zhang,&nbsp;Kun Zhu","doi":"10.1111/sapm.12787","DOIUrl":"https://doi.org/10.1111/sapm.12787","url":null,"abstract":"<div>\u0000 \u0000 <p>We classify all bifurcation phenomena of the flow near a transcritical singularity in planar singularly perturbed differential systems that do not have a breaking parameter via qualitative analysis and blow-up technique. Here, the directional blown up vector fields can have several singularities and no first integral that are different from those in the literatures. The obtained local bifurcations are also illustrated by numerical simulations through a modified Leslie–Gower model, whose global dynamics is thereby obtained.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714709","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.12592","DOIUrl":"https://doi.org/10.1111/sapm.12592","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12592","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142641560","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":"Turing Instability and Dynamic Bifurcation for the One-Dimensional Gray–Scott Model","authors":"Yuncherl Choi,&nbsp;Taeyoung Ha,&nbsp;Jongmin Han,&nbsp;Sewoong Kim,&nbsp;Doo Seok Lee","doi":"10.1111/sapm.12786","DOIUrl":"https://doi.org/10.1111/sapm.12786","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We study the dynamic bifurcation of the one-dimensional Gray–Scott model by taking the diffusion coefficient &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;annotation&gt;${lambda }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the reactor as a bifurcation parameter. We define a parameter space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(k,F)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for which the Turing instability may happen. Then, we show that it really occurs below the critical number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${lambda }_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and obtain rigorous formula for the bifurcated stable patterns. When the critical eigenvalue is simple, the bifurcation leads to a continuous (resp. jump) transition for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${lambda }&amp;lt;{lambda }_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$A_m(k,F)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is negative (resp. positive). We prove that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$A_m(k,F)&amp;gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142724211","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":"On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity","authors":"Filippo Dell'Oro,&nbsp;Lorenzo Liverani,&nbsp;Vittorino Pata,&nbsp;Ramon Quintanilla","doi":"10.1111/sapm.12784","DOIUrl":"https://doi.org/10.1111/sapm.12784","url":null,"abstract":"<p>In this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations\u0000\u0000 </p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12784","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714696","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":"Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method","authors":"Stephen C. Anco,&nbsp;James Hornick,&nbsp;Sicheng Zhao,&nbsp;Thomas Wolf","doi":"10.1111/sapm.12768","DOIUrl":"https://doi.org/10.1111/sapm.12768","url":null,"abstract":"<p>A new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$p=1,2,3,4$</annotation>\u0000 </semantics></math>. No solutions for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p&amp;gt;1$</annotation>\u0000 </semantics></math> were known previously in the literature. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p=1$</annotation>\u0000 </semantics></math>, four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations  as well as to nonlinear ODE systems of generalized Hénon–Heiles form.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12768","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714695","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":"Rogue wave patterns associated with Adler–Moser polynomials featuring multiple roots in the nonlinear Schrödinger equation","authors":"Huian Lin,&nbsp;Liming Ling","doi":"10.1111/sapm.12782","DOIUrl":"https://doi.org/10.1111/sapm.12782","url":null,"abstract":"<p>In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including modified claw-like, one triple root (OTR)-type, modified OTR-type, two triple roots (TTR)-type, semimodified TTR-type, and modified TTR-type patterns. A correlation is established between these rogue wave patterns and the root structures of the Adler–Moser polynomials with multiple roots. At the positions in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x,t)$</annotation>\u0000 </semantics></math>-plane corresponding to simple roots of the Adler–Moser polynomials, these high-order rogue wave patterns asymptotically approach first-order rogue waves. At the positions in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x,t)$</annotation>\u0000 </semantics></math>-plane corresponding to multiple roots of the Adler–Moser polynomials, these rogue wave patterns asymptotically tend toward lower-order fundamental rogue waves, dispersed first-order rogue waves, or mixed structures of these rogue waves. These structures are related to the root structures of special Adler–Moser polynomials with new free parameters, such as the Yablonskii–Vorob'ev polynomial hierarchy, among others. Notably, the positions of the fundamental lower-order rogue waves or mixed structures in these rogue wave patterns can be controlled freely under specific conditions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714712","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":"Orthogonal Laurent Polynomials of Two Real Variables","authors":"Ruymán Cruz-Barroso,&nbsp;Lidia Fernández","doi":"10.1111/sapm.12783","DOIUrl":"https://doi.org/10.1111/sapm.12783","url":null,"abstract":"&lt;p&gt;In this paper, we consider an appropriate ordering of the Laurent monomials &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$x^{i}y^{j}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$i,j in mathbb {Z}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; that allows us to study sequences of orthogonal Laurent polynomials of the real variables &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;annotation&gt;$x$&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;mi&gt;y&lt;/mi&gt;\u0000 &lt;annotation&gt;$y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with respect to a positive Borel measure &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; defined on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;mo&gt;∪&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∩&lt;/mo&gt;\u0000 &lt;mi&gt;supp&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;∅&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(lbrace x=0 rbrace cup lbrace y=0 rbrace) cap textrm {supp}(mu)= emptyset$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This ordering is suitable for considering the &lt;i&gt;multiplication plus inverse multiplication operator&lt;/i&gt; on each variable &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12783","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714669","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":"Rich dynamics of a hepatitis C virus infection model with logistic proliferation and time delays","authors":"Ke Guo,&nbsp;Wanbiao Ma","doi":"10.1111/sapm.12781","DOIUrl":"https://doi.org/10.1111/sapm.12781","url":null,"abstract":"<p>In this paper, we study a dynamic model of hepatitis C virus (HCV) infection with density-dependent proliferation of uninfected and infected hepatocytes and two time delays, which is derived from a three-dimensional model by the quasi-steady-state approximation. The model can exhibit forward bifurcation or backward bifurcation, and an explicit control threshold parameter <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>c</mi>\u0000 </msub>\u0000 <annotation>$R_c$</annotation>\u0000 </semantics></math> is obtained for the case of backward bifurcation. It is shown that if the proliferation rate of infected hepatocytes is greater than the proliferation rate of uninfected hepatocytes by a certain amount, it becomes more difficult for the virus to be removed. The model has rich dynamical properties: (i) In some parameter regions, bistability can occur; (ii) both time delays <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$tau _{1}$</annotation>\u0000 </semantics></math> (virus-to-cell delay) and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$tau _{2}$</annotation>\u0000 </semantics></math> (cell-to-cell delay) can lead to Hopf bifurcations; (iii) same length of time delays <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$tau _{1}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$tau _{2}$</annotation>\u0000 </semantics></math> can lead to at most one stability switch, but different time delays can lead to multiple stability switches. Several sufficient conditions for the global stability of the disease-free equilibrium and the endemic equilibrium are obtained for both forward and backward bifurcation scenarios. In particular, several sharp results on global stability are obtained. Theoretical and numerical results portray the complexity of viral evolutionary dynamics in chronic HCV-infected patients.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714668","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":"Explicit exact solutions for plane shock waves in dilute polyatomic gases","authors":"F. J. Uribe,&nbsp;R. M. Velasco,&nbsp;W. Marques Jr.","doi":"10.1111/sapm.12776","DOIUrl":"https://doi.org/10.1111/sapm.12776","url":null,"abstract":"<p>The exact solutions for the Navier–Stokes–Fourier equations in the case of plane shock waves for dilute monatomic gases with constant transport coefficients were found by Becker in 1922. The solutions obtained are limited for a Prandtl's number given by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 <mo>/</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$Pr=3/4$</annotation>\u0000 </semantics></math>. Besides the solutions for the speed and temperature, profiles were given in an implicit way. In this paper, we consider Becker's model to find some exact <i>explicit</i> solutions for dilute polyatomic gases.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642373","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":"Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind-forced ocean waves","authors":"Agissilaos Athanassoulis,&nbsp;Theodoros Katsaounis,&nbsp;Irene Kyza","doi":"10.1111/sapm.12774","DOIUrl":"https://doi.org/10.1111/sapm.12774","url":null,"abstract":"<p>We consider a nonconservative nonlinear Schrödinger equation (NCNLS) with time-dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time under explicit balance laws. In this paper, we extend to the particular NCNLS two numerical schemes which are known to conserve energy and mass in the discrete level for the cubic nonlinear Schrödinger equation. Both schemes are second-order accurate in time, and we prove that their extensions satisfy discrete versions of the mass and energy balance laws for the NCNLS. The first scheme is a relaxation scheme that is linearly implicit. The other scheme is a modified Delfour–Fortin–Payre scheme, and it is fully implicit. Numerical results show that both schemes capture robustly the correct values of mass and energy, even in strongly nonconservative problems. We finally compare the two numerical schemes and discuss their performance.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642372","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}