Studies in Applied Mathematics最新文献

{"title":"On a Class of Viscoelastic Plate Equations Modeling the Oscillations of Suspension Bridges","authors":"Yang Liu,&nbsp;Runzhang Xu,&nbsp;Chao Yang","doi":"10.1111/sapm.70195","DOIUrl":"https://doi.org/10.1111/sapm.70195","url":null,"abstract":"<div>\u0000 \u0000 <p>To well understand the characteristics of the oscillations of suspension bridges, we consider a class of viscoelastic plate equations with mixed boundary conditions consisting of simply supported and free boundary conditions to study the interactions between the viscoelastic dissipation, restoring force, frictional damping, and nonlinear source terms and their effects on the dynamical behavior of solution. Based on the so-called potential well theory, we obtain the global existence and exponential decay of solution with positive initial energy that is less than the potential well depth. By weakening the viscoelastic dissipation so that the nonlinear source term is dominant, we obtain the finite-time blowup of solution with negative initial energy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 <mo>&lt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$E(0)&lt;0$</annotation>\u0000 </semantics></math> and null initial energy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$E(0)=0$</annotation>\u0000 </semantics></math>, respectively. By further weakening the viscoelastic dissipation, we derive the finite-time blowup of solution with positive initial energy controlled by the shrunk potential well depth <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$theta d$</annotation>\u0000 </semantics></math>. In addition, we provide estimates on the upper bound of the blow-up time.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147564632","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 a Matrix-Constrained CKP Hierarchy","authors":"Song Li,&nbsp;Kelei Tian,&nbsp;Zhiwei Wu","doi":"10.1111/sapm.70192","DOIUrl":"https://doi.org/10.1111/sapm.70192","url":null,"abstract":"<div>\u0000 \u0000 <p>The algebraic structures of integrable hierarchies play an important role in the study of soliton equations. In this paper, we use splitting theory to give a matrix representation of a constrained CKP hierarchy, which can be considered as a generalization of the <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mover>\u0000 <mi>A</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <annotation>$hat{A}_{2n}^{(2)}$</annotation>\u0000 </semantics></math>-KdV hierarchy and the constrained KP hierarchy. An equivalent construction in terms of the pseudo-differential operator is discussed. Darboux transformations, scaling transformations, and tau functions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ln</mi>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mi>f</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$ln tau _f$</annotation>\u0000 </semantics></math> for this constrained hierarchy are studied.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563565","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.70196","DOIUrl":"https://doi.org/10.1111/sapm.70196","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563566","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":"A Decompositional Approach for Two-Dimensional, Two-Phase, Nonlinear Inverse Stefan Problems Using the Method of Fundamental Solutions","authors":"Gujji Murali Mohan Reddy,&nbsp;Phalguni Nanda,&nbsp;Michael Vynnycky","doi":"10.1111/sapm.70184","DOIUrl":"10.1111/sapm.70184","url":null,"abstract":"<p>In this paper, we propose a decompositional (phase-wise split) approach to solve a two-dimensional, two-phase (solid and liquid, say), nonlinear inverse Stefan problem. The first step is to approximate the unknown moving boundary between the two phases and the Stefan condition on that boundary using the overspecified boundary and initial data on the solid. The second and final step is then to reconstruct the temperature and heat flux on the fixed liquid boundary using the approximated Stefan conditions and given initial data. In each phase, we obtain the Tikhonov-regularized approximations using the method of fundamental solutions (MFS) and formulate heuristic residual a posteriori estimators to quantify the errors in the approximations. The MFS parameters for controlling the error are detected automatically in a systematic way, by virtue of a mean-filtering algorithm and a deterministic optimization strategy; this is in stark contrast to the less systematic way employed in existing nonlinear optimization algorithms. Numerical results demonstrate the effectiveness of the proposed approach.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70184","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147649444","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":"The Variable-Length Stem Structures in Three-Soliton Resonance of the Kadomtsev–Petviashvili II Equation","authors":"Feng Yuan,&nbsp;Jingsong He,&nbsp;Yi Cheng","doi":"10.1111/sapm.70194","DOIUrl":"10.1111/sapm.70194","url":null,"abstract":"<div>\u0000 \u0000 <p>The stem structure is a localized feature that arises during high-order soliton interactions, connecting the vertices of two V-shaped waveforms. The interaction of resonant 3-solitons is accompanied by soliton reconnection phenomena, characterized by the disappearance and reconnection of stem structures. This paper investigates variable-length stem structures in resonant 3-soliton solutions of the Kadomtsev–Petviashvili II (KPII) equation, focusing on both 2-resonant and 3-resonant 3-soliton cases. Depending on the phase shift tends to plus/minus infinity, different types of resonances are identified, including strong resonance, weak resonance, and mixed (strong-weak) resonance. We derive and analyze the asymptotic forms and explicit expressions for the soliton arm trajectories, velocities, as well as the endpoints, length, and amplitude of the stem structures. A detailed comparison is made between the similarities and differences of the stem structures in the 2-resonant and 3-resonant solitons. In addition, we provide a comprehensive and rigorous analysis of both the asymptotic behavior and the structural properties of the stems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147649446","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":"Extending Slow Manifolds to Nonhyperbolic Points in Planar Singularly Perturbed Systems When Linearly Slow Flow Has No Directions","authors":"Kun Zhu,&nbsp;JianHe Shen,&nbsp;Yi Zhang","doi":"10.1111/sapm.70193","DOIUrl":"10.1111/sapm.70193","url":null,"abstract":"<div>\u0000 \u0000 <p>By employing geometric singular perturbation theory along with the techniques of blow-up and generalized rotated vector field, this paper aims to extend the slow flow to nonhyperbolic points in planar singularly perturbed systems. We are mainly concerned with a more degenerate situation, where the linearly slow flow has no direction. Under this setting, this paper gives a classification of the flow near transcritical singularity, which is a typical nonhyperbolic point in planar singularly perturbed systems. This more degenerate case gives rise to new dynamical behaviors, such as the slow flow exhibiting opposite direction relative to the reduced flow on critical manifold after perturbation. Numerical simulations of two examples are also carried out to verify the theoretical predictions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147649445","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":"Maxwell Fronts in the Discrete Nonlinear Schrödinger Equations With Competing Nonlinearities","authors":"Farrell Theodore Adriano,&nbsp;Hadi Susanto","doi":"10.1111/sapm.70191","DOIUrl":"10.1111/sapm.70191","url":null,"abstract":"<p>In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schrödinger (DNLS) equations are often employed to model these dynamics, particularly in the context of Bose–Einstein condensates and optical waveguide arrays. While the classical DNLS with cubic nonlinearity admits well-known solitonic solutions, the introduction of competing nonlinearities, such as quadratic–cubic and cubic–quintic terms, gives rise to new behaviors, including multistability and front formation. One such emergent structure, the Maxwell front, is characterized by stationary interfaces between two energetically equivalent steady states, occurring at a critical parameter known as the Maxwell point. This paper investigates the existence and stability of Maxwell fronts in DNLS models with competing nonlinearities. Specifically, we examine the quadratic–cubic nonlinearity, as found in the discrete quantum droplets equation, and the cubic–quintic nonlinearity, both of which exhibit multistability. We explore the persistence of Maxwell fronts in both the anticontinuum limit (where the coupling between lattice sites is weak) and the continuum limit (where the coupling is strong). The stability of these fronts is analyzed through linear stability analysis, utilizing eigenvalue counting arguments and exponential asymptotic techniques. Our results provide new insights into multistability, front dynamics, and the role of competing nonlinearities in discrete wave systems. The main contributions of this work include the characterization of Maxwell fronts in DNLS equations with competing nonlinearities, the analysis of their stability across different coupling regimes, and the application of novel asymptotic methods to investigate their behavior in the continuum limit.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147649413","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":"Long-Time Asymptotics for the Modified Camassa–Holm Positive Flow With the Schwartz Initial Data","authors":"Kedong Wang,&nbsp;Xianguo Geng","doi":"10.1111/sapm.70189","DOIUrl":"https://doi.org/10.1111/sapm.70189","url":null,"abstract":"<div>\u0000 \u0000 <p>The Cauchy problem of the modified Camassa–Holm (CH) positive flow with the Schwartz initial data is studied by using the Riemann–Hilbert (RH) approach and nonlinear steepest descent method. Due to the existence of energy-dependent potential, the spectral analysis of Lax pairs is extremely difficult. We have to go out of our way and introduce some spectral function transformations, from which a basic RH problem is constructed with the aid of the inverse scattering transformation. Then we convert the basic RH problem into a regular RH problem and take into account the reorientation, local parametrices, and main contributions. Finally, we obtain the long-time asymptotic behavior of solution of the modified CH positive flow.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147320791","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":"Analysis and Simulation of an Improved Fast Two-Grid Mixed Element Method for a Nonlinear Time Fractional Pseudo-Hyperbolic Equation","authors":"Yining Yang,&nbsp;Nian Wang,&nbsp;Cao Wen,&nbsp;Hong Li,&nbsp;Yang Liu","doi":"10.1111/sapm.70182","DOIUrl":"https://doi.org/10.1111/sapm.70182","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, an improved fast two-grid mixed element algorithm is developed for a nonlinear time fractional pseudo-hyperbolic wave equation model. By introducing two auxiliary variables, the original problem is transformed into a lower-order coupled system with three equations, and then a fully discrete nonlinear mixed element system is formulated, where the spatial direction is approximated by the provided mixed element method, and the temporal direction is discretized using the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 <mo>−</mo>\u0000 <msub>\u0000 <mn>1</mn>\u0000 <mi>σ</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$L2-1_{sigma }$</annotation>\u0000 </semantics></math> approximation. To further address the computational time issue caused by nonlinear iterations, a fast two-grid mixed finite element algorithm in space is constructed. The stability and error estimates for the fully discrete improved fast two-grid mixed element algorithm are derived. Finally, by the comparison with the computing results of the nonlinear mixed element algorithm, it is evident that the proposed two-grid mixed finite element algorithm significantly improves computational efficiency.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147280949","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 Initial-Boundary Value Problem of Klein–Gordon Equation on the Half-Line","authors":"Tao Zhang,&nbsp;Shou-Fu Tian","doi":"10.1111/sapm.70188","DOIUrl":"https://doi.org/10.1111/sapm.70188","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This work investigates the initial-boundary value problem (IBVP) of the Klein–Gordon (KG) equation on the half-line within the Sobolev spaces framework. By employing the Fokas method coupled with the Banach fixed-point theorem, we establish the following key results: (i) For the IBVP of linear KG equation, we prove the well-posedness results through decomposition into a free Cauchy problem and a forced IBVP with homogeneous data. A priori linear estimates for these decomposed problems are rigorously derived. (ii) The IBVP of the nonlinear KG equation is systematically analyzed via the Banach fixed-point theorem in the space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mrow&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;msup&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;*&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&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;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$C([0,T^ast]; H^s_x(0,infty))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, which establishes local well-posedness under the regularity condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$frac{1}{2}&lt;s&lt;frac{5}{2}$&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;s&lt;/mi&gt;\u0000 &lt;mo&gt;≠&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sne frac{3}{2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. (iii) A synthesis of the Fokas method with Sobolev spaces techniques extends the applicability of the Fokas method to fractional regularity regimes. The methodology provides explicit solution representations while maintaining appropriate regularity matching between initial and boundary data. This work significantly advances the functional framework for IBVP analysis on unbounded domains, bridging modern transform","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147275020","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}