Studies in Applied Mathematics最新文献

{"title":"Emergence of Well-Ordering and Clustering for a First-Order Nonlinear Consensus Model","authors":"Junhyeok Byeon,&nbsp;Seung-Yeal Ha,&nbsp;Myeongju Kang,&nbsp;Wook Yoon","doi":"10.1111/sapm.70006","DOIUrl":"https://doi.org/10.1111/sapm.70006","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the predictability of asymptotic clustering patterns in a first-order nonlinear consensus model on receiver network on the real line. Nonlinear couplings between particles (agents) are characterized by an odd, locally Lipschitz, and increasing function. The proposed consensus model and its clustering dynamics is motivated by the one-dimensional Cucker–Smale flocking model. Despite the complexity registered by heterogeneous couplings, we provide a sufficient framework to predict asymptotic dynamics such as particles' aggregation, segregation, and clustering patterns. We also verify the robustness of clustering patterns to structural changes such as relativistic effects implemented by the suitable composition of functions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113833","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":"Traveling Viral Waves for a Spatial May–Nowak Model with Hybrid Local and Nonlocal Dispersal","authors":"Jie Wang,&nbsp;Jinfen Guo,&nbsp;Chuanhui Zhu,&nbsp;Shuang-Ming Wang","doi":"10.1111/sapm.70007","DOIUrl":"https://doi.org/10.1111/sapm.70007","url":null,"abstract":"<div>\u0000 \u0000 <p>To investigate the spatial dynamics of viruses propagating between host cells, the current paper is devoted to studying the existence and nonexistence of viral waves for a reaction–diffusion and May–Nowak system with hybrid dispersal. Specifically, we define a critical wave speed <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$ c^{ast }$</annotation>\u0000 </semantics></math> threshold to determine the existence of traveling waves when the viral infection reproduction number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$ mathcal {R}_{0}&gt;1$</annotation>\u0000 </semantics></math>. By employing the upper/lower solutions along with the Schauder's fixed-point theorem, the existence of traveling waves connecting the uninfected and infected states is determined for each wave speed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 <mo>≥</mo>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ cge c^{ast }$</annotation>\u0000 </semantics></math>. Conversely, nonexistence is demonstrated through the application of the negative one-sided Laplace transform for the case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>c</mi>\u0000 <mo>&lt;</mo>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ 0 &lt; c &lt; c^{ast }$</annotation>\u0000 </semantics></math>. The nonexistence of traveling waves in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {R}_{0}le 1$</annotation>\u0000 </semantics></math> case is also demonstrated. Finally, some novel coupled numerical algorithms are developed to analyze the traveling viral waves and asymptotic spreading speed of the model on account of the actual hybrid dispersal features, which strongly shows that the introduction of nonlocal dispersal will accelerate viral infection.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112379","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":"Solving a Singular Limit Problem Arising With Euler–Korteweg Dispersive Waves","authors":"Quentin Didierlaurent,&nbsp;Nicolas Favrie,&nbsp;Bruno Lombard","doi":"10.1111/sapm.70005","DOIUrl":"https://doi.org/10.1111/sapm.70005","url":null,"abstract":"<div>\u0000 \u0000 <p>Phase transition in compressible flows involves capillarity effects, described by the Euler–Korteweg (EK) equations with nonconvex equation of state. Far from phase transition, that is, in the two convex parts of the equation of state, the dispersion terms vanish and one should recover the hyperbolic Euler equations of fluid dynamics. However, the solution of EK equations does not converge toward the solution of Euler equations when dispersion tends toward zero while being nonnull: it is a singular limit problem. To avoid this issue in the case of convex equation of state, a Navier–Stokes–Korteweg (NSK) model is considered, whose viscosity is chosen to counterbalance exactly the dispersive terms. In the limit of small viscosity and small dispersion, the Euler model is recovered. Numerically, an extended Lagrangian method is used to integrate the NSK equations so obtained. Doing so allows to use classical numerical schemes of Godunov type with source term. Numerical results for a Riemann problem illustrate the convergence properties with vanishing dispersion.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121149","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":"Uniform Asymptotic Expansions for the Zeros of Parabolic Cylinder Functions","authors":"T. M. Dunster,&nbsp;Amparo Gil,&nbsp;Diego Ruiz-Antolin,&nbsp;Javier Segura","doi":"10.1111/sapm.70004","DOIUrl":"https://doi.org/10.1111/sapm.70004","url":null,"abstract":"<div>\u0000 \u0000 <p>The real and complex zeros of the parabolic cylinder function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$U(a,z)$</annotation>\u0000 </semantics></math> are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for <span></span><math>\u0000 <semantics>\u0000 <mi>a</mi>\u0000 <annotation>$a$</annotation>\u0000 </semantics></math> positive or negative and large in absolute value, uniformly for unbounded <span></span><math>\u0000 <semantics>\u0000 <mi>z</mi>\u0000 <annotation>$z$</annotation>\u0000 </semantics></math> (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121150","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":"Auto-Bäcklund Transformations for New Matrix First and Second Painlevé Hierarchies","authors":"Pilar Ruiz Gordoa,&nbsp;Andrew Pickering","doi":"10.1111/sapm.70002","DOIUrl":"https://doi.org/10.1111/sapm.70002","url":null,"abstract":"<div>\u0000 \u0000 <p>We define a new doubly extended matrix second Painlevé hierarchy, and in addition a new extended matrix first Painlevé hierarchy. For the former, we present three auto-Bäcklund transformations (auto-BTs) that constitute nontrivial extensions to our new hierarchy of previously derived results on the auto-BTs of a much simpler matrix second Painlevé hierarchy; for the latter, we define an auto-BT analagous to the third of these matrix second Painlevé auto-BTs. In addition, for both of our new hierarchies, we define a new class of auto-BT. In the scalar reduction, these then give rise to a new Bäcklund process for the second Painlevé equation, as well as to a similar Bäcklund process for the first Painlevé equation. These new Bäcklund processes provide mappings of arbitrary constants appearing in solutions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121151","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 Riemann Problem for the Flow Pattern in Deviated Pipes Carrying Isentropic Two-Phase Flows","authors":"Sarswati Shah","doi":"10.1111/sapm.70003","DOIUrl":"https://doi.org/10.1111/sapm.70003","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the Riemann problem for the one-dimensional two-phase isentropic flow in deviated pipes. The model under consideration is nonconservative and conditionally strictly hyperbolic. The generalized Rankine–Hugoniot conditions are established for the present system with nonconservative products to define weak solutions. Exact Riemann solutions are presented in fully explicit forms for the nonhomogeneous model, where the elementary waves are discussed along parabolic curves. Moreover, it is demonstrated that a delta shock wave appears in the Riemann solutions under specific conditions when the pressure vanishes.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120790","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":"Two-Dimensional Fractional Discrete Nonlinear Schrödinger Equations: Dispersion Relations, Rogue Waves, Fundamental, and Vortex Solitons","authors":"Ming Zhong,&nbsp;Boris A. Malomed,&nbsp;Jin Song,&nbsp;Zhenya Yan","doi":"10.1111/sapm.70001","DOIUrl":"https://doi.org/10.1111/sapm.70001","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators based on an appropriately modified definition of the continuous Riesz fractional derivative. The model of the 2D isotropic lattice employs the discrete fractional Laplacian, whereas the 2D anisotropic system incorporates discrete fractional derivatives acting independently along orthogonal directions with different Lévy indices (LIs). We derive exact linear dispersion relations (DRs), and identify spectral bands that permit linear modes to exist, finding them to be similar to their continuous counterparts, apart from differences in the wavenumber range. Additionally, the modulational instability in the discrete models is studied in detail, and, akin to the linear DRs, it is found to align with the situation in continuous models. This consistency highlights the nature of our newly defined discrete fractional derivatives. Furthermore, using Gaussian inputs, we produce a variety of rogue-wave structures. By means of numerical methods, we systematically construct families of 2D fundamental and vortex solitons, and examine their stability. Fundamental solitons maintain the stability due to the discrete nature of the interactions, preventing the onset of the critical and supercritical collapse. On the other hand, vortex solitons are unstable in the isotropic lattice model. However, the anisotropic one—in particular, its symmetric version with equal LIs acting in both directions—maintains stable vortex solitons with winding numbers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$S=1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$S=3$</annotation>\u0000 </semantics></math>. The detailed results stress the robustness of the newly defined discrete fractional Laplacian in supporting well-defined soliton modes in the 2D lattice media.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861651","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":"Variable-Coefficient Evolution Problems via the Fokas Method Part I: Dissipative Case","authors":"Bernard Deconinck,&nbsp;Matthew Farkas","doi":"10.1111/sapm.12800","DOIUrl":"https://doi.org/10.1111/sapm.12800","url":null,"abstract":"<div>\u0000 \u0000 <p>We derive explicit solution representations for linear, dissipative, second-order initial-boundary value problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We accomplish this by considering the variable-coefficient problem as the limit of a constant-coefficient interface problem, previously solved using the unified transform method of Fokas. Our method produces an explicit representation of the solution, allowing us to determine properties of the solution directly. As explicit examples, we demonstrate the solution procedure for different IBVPs of variations of the heat equation, and the linearized complex Ginzburg-Landau (CGL) equation (periodic boundary conditions). We can use this to find the eigenvalues of dissipative second-order linear operators (including non–self-adjoint ones) as roots of a transcendental function, and we can write their eigenfunctions explicitly in terms of the eigenvalues.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861440","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":"Concentric-Ring Patterns of Higher-Order Lumps in the Kadomtsev–Petviashvili I Equation","authors":"Bo Yang,&nbsp;Jianke Yang","doi":"10.1111/sapm.70000","DOIUrl":"https://doi.org/10.1111/sapm.70000","url":null,"abstract":"<p>Large-time patterns of general higher-order lump solutions in the Kadomtsev–Petviashvili I (KP-I) equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x, y)$</annotation>\u0000 </semantics></math>-plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian–Hermite polynomial, together with possible fundamental lumps in the inner region that are uniformly distributed on concentric rings generically. Leading-order predictions of fundamental lumps in these solution patterns are also derived. The predicted patterns at large times are compared to true solutions, and good agreement is observed.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861441","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":"On Global and Decay Solution of Viscous Compressible MHD Equations","authors":"Rachid Benabidallah,&nbsp;François Ebobisse,&nbsp;Mohamed Azouz","doi":"10.1111/sapm.12794","DOIUrl":"https://doi.org/10.1111/sapm.12794","url":null,"abstract":"<p>We consider in an infinite horizontal layer, the equations of the viscous compressible magnetohydrodynamic flows subject to the gravitational force. On the upper and lower planes of the layer, we consider homogeneous Dirichlet conditions on the velocity while a large constant vector field is prescribed on the magnetic field. The existence of the global strong solution with small initial data and its asymptotic behavior as time goes to infinity are established.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12794","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860887","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}