Studies in Applied Mathematics最新文献

{"title":"Evolution of an Incompressible Fluid Drop Under a Central Force Field: Analytical Benchmark Solutions for Free-Surface Flows","authors":"Matteo Antuono","doi":"10.1111/sapm.70249","DOIUrl":"https://doi.org/10.1111/sapm.70249","url":null,"abstract":"<p>We present a set of exact and approximate analytical solutions describing the evolution of a fluid drop under the action of a central force field, in both two and three dimensions. The fluid is assumed to be Newtonian and incompressible with a free surface and no solid boundaries The absence of solid walls eliminates boundary-layer effects, enabling focused analysis of free-surface dynamics. The benchmarks address key phenomena: nonlinear surface deformation, viscous damping and vorticity, and small-amplitude oscillations under viscosity and surface tension. Designed for minimal complexity and straightforward implementation, these cases provide rigorous conditions for evaluating the accuracy and stability of numerical solvers, supporting reliable computational fluid dynamics validation and fundamental studies of free-surface flows.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70249","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148324625","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":"Selective Convergence of Followers to Multiple Leaders With Repulsion and Cohesion on Riemannian Manifolds","authors":"Hyunjin Ahn","doi":"10.1111/sapm.70252","DOIUrl":"https://doi.org/10.1111/sapm.70252","url":null,"abstract":"<p>We study the long-term dynamics of followers that selectively follow one of multiple leaders on Riemannian manifolds, where the leaders interact through repulsive forces while remaining cohesively bounded. We propose a multileader–follower multiagent system defined on Riemannian manifolds. In our model, each follower chooses exactly one leader among several leaders and follows it, while the leaders interact with each other through repulsive forces that prevent collisions but do not allow excessive dispersion. Through follower–leader interactions, each group of followers converges to its corresponding leader. For the theoretical analysis, we review the Rauch Comparison Theorem and the main geometric concepts related to it. We also introduce the classical Barbalat Lemma. Furthermore, we extend the Barbalat Lemma to a manifold setting so that it can be applied to vector fields on Riemannian manifolds. We then present several sufficient conditions on the initial data, system parameters, and kernel functions. Using a suitable energy function, we obtain several energy estimates, which in particular guarantee collision avoidance among the leaders and leader cohesion in the sense that the interleader distances remain uniformly bounded. By combining these energy estimates with the Rauch Comparison Theorem, the classical Barbalat Lemma, and its manifold extension developed in this paper, we rigorously prove that each selectively assigned group of followers asymptotically converges to its corresponding leader on Riemannian manifolds. Finally, we provide numerical simulations to validate and illustrate our theoretical results.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70252","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282128","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":"Rigorous Analytical Solution for the Linearized Whitham–Broer–Kaup System on the Half-Line","authors":"Andreas Chatziafratis,&nbsp;Georgia Karali,&nbsp;Costas E. Synolakis","doi":"10.1111/sapm.70237","DOIUrl":"https://doi.org/10.1111/sapm.70237","url":null,"abstract":"<div>\u0000 \u0000 <p>The higher-order Whitham–Broer–Kaup (WBK) system is a pair of coupled nonlinear evolution partial differential equations (PDEs) describing the interaction between long and short dispersive waves in shallow water. We solve explicitly, via a suitable implementation of the Fokas unified transform method, fully nonhomogeneous initial-boundary-value problems for the linearized WBK system formulated on a spatiotemporal quarter-plane. Our novel closed-form integral representations are expressed as contour integrals in the spectral Fourier plane and verified a posteriori. In addition to solving the canonical problem, analogous analytical formulas are obtained for a problem with nonstandard boundary conditions. Despite the asymmetry of the system, all solutions are shown to have Schrödinger-type analytic properties, which in turn imply a dynamic behavior analogous to what Chatziafratis, Ozawa, and Tian (<i>Mathematische Annalen</i> 389, 2023) reported for the solution of the classical free-space time-dependent Schrödinger equation. This work is also useful in the study of well-posedness for the nonlinear analog.</p>\u0000 </div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174511","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":"Global Dynamics in Planar Piecewise Linear Hysteretic Systems","authors":"Shimin Li,&nbsp;Qian Tong,&nbsp;Wencheng Wu,&nbsp;Wanqi Zheng","doi":"10.1111/sapm.70248","DOIUrl":"https://doi.org/10.1111/sapm.70248","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the global dynamics of planar piecewise linear hysteretic systems. First, we analyze the Hopf bifurcation in a general piecewise linear hysteretic systems, corresponding to the classification HLB17 in Simpsons taxonomy (Simpson, 2022, Physics Reports), and then deduced the stability criteria via the derivative of Poincaré map. Next, we examine a symmetric subclass of such systems, known as planar feedback systems, and prove that they admit at most one limit cycle. Furthermore, we provide a complete characterization of global phase portraits in the Poincaré disk, elucidating their topological structure.</p>\u0000 <p>As an application, we construct a physical model consisting of a metal ball confined within a pipe and subjected to magnetic forces from symmetrically placed contacts. This setup yields a planar feedback system, and our analysis reveals two distinct regimes of periodic motion, depending on the relative strength of the magnetic interactions. A comprehensive bifurcation diagram is derived, delineating the transition between these dynamical behaviors.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174075","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":"Second and Third Harmonic Generation of Elastic Waves in a Nonlinear Solid Under Shear Loading","authors":"Fernando Lund","doi":"10.1111/sapm.70247","DOIUrl":"https://doi.org/10.1111/sapm.70247","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The problem of nonlinear generation of a second harmonic longitudinal—acoustic—wave propagating along one direction, “&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;”, but with an external transverse—shear—monochromatic localized load of amplitude &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${S}_{0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, is solved to second and third order in the nonlinearities through a successive approximation scheme. The longitudinal wave so generated, of amplitude &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;${S}_{0}^{2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, is the superposition of two monochromatic waves of frequency &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$2{omega}_{0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${omega}_{0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the loading frequency. One of the waves travels with the speed of linear longitudinal waves and the other with the speed of linear shear waves. An alternative description is to say that the result is an amplitude-modulated wave of frequency &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$2{omega}_{0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with the carrier wave traveling at a speed that is twice the harmonic mean of the longitudinal and transverse velocities, and the modulating wave has a wavelength &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;λ&lt;/mi&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174074","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":"Exact Solutions for Delta-Shock Wave Interactions in a Magnetohydrodynamics Model","authors":"Adelino Paiva","doi":"10.1111/sapm.70245","DOIUrl":"https://doi.org/10.1111/sapm.70245","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper analyzes delta-shock wave interactions in a one-dimensional model of magnetohydrodynamics (MHD) described by a nonlinear hyperbolic system of conservation laws. The study is conducted within a distributional framework that generalizes the classical weak solution concept, allowing for Dirac delta-type initial data. A Cauchy problem formulated as a Riemann problem with singularities in both state variables is solved exactly. The resulting solutions display coherent, soliton-like dynamics, and a subclass of distributional solitons is identified as a special case of delta-shock waves. These findings advance the analytical understanding of nonlinear conservation laws with singular data and shed light on novel wave structures in MHD.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148153620","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.70250","DOIUrl":"https://doi.org/10.1111/sapm.70250","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148153622","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":"Generalized Riemann Problem and Nonlinear Wave Interactions in Macroscopic Production Model","authors":"Lilu Sahu,&nbsp;T. Raja Sekhar,&nbsp;G. P. Raja Sekhar","doi":"10.1111/sapm.70246","DOIUrl":"https://doi.org/10.1111/sapm.70246","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we examine a system of hyperbolic balance laws governing macroscopic production model which describes high-volume product flows. Our primary focus is on the nonlinear wave interactions involving shock and rarefaction. Employing the theory of differential constraints, we first demonstrate that the governing system is compatible with a set of differential constraints, which allows us to handle the nonhomogeneous term by making the governing system diagonalized. We show that the governing system admits a strictly convex entropy–entropy flux pair which leads to the well-posedness of the solution. Furthermore, we obtain the solution, that consists of shocks and rarefaction waves, of the Riemann problem as well as the generalized Riemann problem. Consequently, we discuss all possible interactions of elementary waves of the Riemann problem. Here, the primary challenge is to identify the solution structure of the generalized Riemann problem which is formed at the time of collision of shocks and rarefaction waves as solution of the Riemann problem. In addition, we implement an upwind-based splitting scheme to validate the analytical results through various test cases.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148153621","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":"Stability of KdV Solitons on the Half-Line: A Study for Nonhomogeneous Boundary Conditions","authors":"Luccas Campos,&nbsp;Mykael Cardoso,&nbsp;Márcio Cavalcante","doi":"10.1111/sapm.70244","DOIUrl":"https://doi.org/10.1111/sapm.70244","url":null,"abstract":"<p>We study the orbital stability and asymptotic stability problems for <i>KdV solitons</i> on the right half-line for nonhomogeneous boundary conditions in the energy space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mo>+</mo>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^1(mathbb {R}^+)$</annotation>\u0000 </semantics></math>. This paper improves the results of Cavalcante and Muñoz [<i>Revista Matemática Iberoamericana</i> 35, no. 6 (2019); and <i>SIAM Journal on Mathematical Analysis</i> 55, no. 5 (2023): 4193–5992], which treat the homogeneous case. One of the key components of the stability argument in this work is the refinement of the estimate for the Lyapunov functional, given that the mass and energy, unlike in the context of homogeneous boundary conditions, do not exhibit a dissipative mechanism. As a consequence of this analysis, we obtain global control of the trace of the first and second derivatives of the solution to the model. This is, as far as we understand, the first orbital and asymptotic stability result for solitons posed on a half-line in the context of nonhomogeneous boundary conditions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 6","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70244","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148153619","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148091893","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}