Studies in Applied Mathematics最新文献

{"title":"Some Exact and Approximate Solutions to a Generalized Maxwell–Cattaneo Equation—Part 2: The Temperature, Heat-Flux System","authors":"Isom H. Herron","doi":"10.1111/sapm.70300","DOIUrl":"https://doi.org/10.1111/sapm.70300","url":null,"abstract":"<div>\u0000 \u0000 <p>The classical heat conduction equation in one-space dimension does not have the property of a finite speed of information transfer. Maxwell found an extension of the equation which Cattaneo also obtained by generalizing the Fourier law of heat conduction. In this work, the time delay rate which Cattaneo defined is taken to be dependent on temperature, satisfying a thermodynamic constraint. The resulting generalized nonlinear Cattaneo system is analyzed in two directions. First, in supporting the existence of traveling waves and second by similarity methods, suitable in the study of an initial-value problem. The results show the emergence of wave fronts propagating from higher to lower temperature regions, as well as self-similar profiles describing diffusive-like behavior.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942623","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":"Mean Field Derivation of a System of Nonlocal Conservation Laws","authors":"Yueying Yang,&nbsp;Li Chen,&nbsp;Wancheng Sheng","doi":"10.1111/sapm.70301","DOIUrl":"https://doi.org/10.1111/sapm.70301","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the mean-field derivation of a multispecies nonlocal conservation laws from an <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> particle Liouville equation incorporating particle interactions. The convergence is established in a strong sense. First, a vanishing viscosity result is provided to demonstrate the convergence of the nonlocal viscous system to its associated nonlocal conservation laws, including both weak and strong convergence. Achieving strong <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> convergence in the vanishing viscosity limit requires a sequence of delicate uniform estimates and Helly's compactness argument. Second, the relative entropy method is employed to justify the strong <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> convergence to the mean field limit in the multispecies setting.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942775","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":"Nonisospectral Deformations of Noncommutative Laurent Biorthogonal Polynomials and Matrix Discrete Painlevé-Type Equations","authors":"Dan Dai,&nbsp;Xiaolu Yue","doi":"10.1111/sapm.70251","DOIUrl":"https://doi.org/10.1111/sapm.70251","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we establish a connection between noncommutative Laurent biorthogonal polynomials (bi-OPs) and matrix discrete Painlevé (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi-OPs to obtain the noncommutative nonisospectral mixed relativistic Toda lattice and its Lax pair. Then, we perform a stationary reduction on this Lax pair to obtain a matrix dP-type equation. The validity of this reduction is demonstrated through a specific choice of weight function and the application of quasideterminant properties. In the scalar case, our matrix dP equation reduces to the known alternate dP II equation.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942096","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":"KPP Dynamics in Predator–Prey Models: A Survey and a Mussel–Algae Case Study","authors":"Anna Ghazaryan,&nbsp;Vahagn Manukian","doi":"10.1111/sapm.70293","DOIUrl":"https://doi.org/10.1111/sapm.70293","url":null,"abstract":"<p>We discuss traveling fronts in several coupled reaction–diffusion systems that model predator–prey interactions, as well as other systems that share similar structural features. We review some cases where the traveling fronts exist and are small perturbations of fronts in certain scalar equations of Fisher–KPP or Burgers–FKPP type.</p><p>As a new result consistent with the reviewed cases, we establish the existence of a previously unobserved family of traveling fronts in a mussel–algae interaction model, in a parameter regime complementary to those studied earlier. These fronts are constructed as perturbations of fronts of a Fisher–KPP-type scalar equation using geometric singular perturbation theory.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70293","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942095","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":"Edge Density Expansions for the Classical Gaussian and Laguerre Ensembles","authors":"Peter J. Forrester,&nbsp;Anas A. Rahman,&nbsp;Bo-Jian Shen","doi":"10.1111/sapm.70295","DOIUrl":"https://doi.org/10.1111/sapm.70295","url":null,"abstract":"<p>Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of the Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes: orthogonal, unitary, and symplectic. In this work we give a different viewpoint on these results in the case of the soft edge scaled density, and in the Laguerre case we initiate an analogous study at the hard edge. Our tool is the scalar differential equation satisfied by the density, known from earlier work. Unlike integral representations, these differential equations in soft edge scaling variables isolate the function of <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> that is the expansion variable. Moreover, they give information on the correction terms which supplements the findings from the work of Bornemann. In the case of the Gaussian ensemble, we can demonstrate analogous features for Dyson index <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>=</mo>\u0000 <mn>6</mn>\u0000 </mrow>\u0000 <annotation>$beta = 6$</annotation>\u0000 </semantics></math>, which suggests a broader class of models, namely the classical <span></span><math>\u0000 <semantics>\u0000 <mi>β</mi>\u0000 <annotation>$beta$</annotation>\u0000 </semantics></math> ensembles, having asymptotic expansions exhibiting integrable features. For the Laguerre ensembles at the hard edge, we give the explicit form of the correction at second order for unitary symmetry, and at first order in the orthogonal and symplectic cases. Various differential relations are demonstrated.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872071","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":"Thin Shell Limit and the Derivation of the Viscosity Operator on the Ellipsoid","authors":"Chi Hin Chan,&nbsp;Magdalena Czubak,&nbsp;Padi Fuster Aguilera","doi":"10.1111/sapm.70296","DOIUrl":"https://doi.org/10.1111/sapm.70296","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the ellipsoid. We show that the general method of the thin shell limit through the asymptotic expansion depends on the averaging method used. We consider both the homogeneous Navier and Hodge boundary conditions. We also obtain a geometric representation of these two boundary conditions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872085","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":"Soliton Solutions to the Coupled Sasa-Satsuma-mKdV Equation","authors":"Changyan Shi,&nbsp;Bao-Feng Feng","doi":"10.1111/sapm.70292","DOIUrl":"https://doi.org/10.1111/sapm.70292","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-modified Korteweg-de Vries (Sasa-Satsuma-mKdV) equation using the Kadomtsev–Petviashvili reduction method. Under zero, nonzero and mixed boundary conditions, we derive four distinct classes of soliton solutions: bright–bright, dark–dark, bright–dark, and dark–bright. These solutions are derived from the vector Hirota equation, for which the bright, dark, and bright–dark soliton solutions are provided in the Appendix. We perform asymptotic analysis of soliton collisions for each class of solutions. Inelastic collisions are observed between bright–bright solitons. In the dark–dark case, the soliton structures are similar to those of the Sasa-Satsuma equation which include double-hole, Mexican hat and anti-Mexican hat solutions. The collision between these solitons and kink solitons and the resonances between dark–dark solitons and breather–breather are new phenomena found in the coupled Sasa-Satsuma-mKdV equation.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872086","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.70304","DOIUrl":"https://doi.org/10.1111/sapm.70304","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70304","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872087","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 Generalized Principal Eigenvalue Approach to Spreading Speeds for Time-Heterogeneous Nonlocal Diffusion Models","authors":"Guan-Qun Wang,&nbsp;Wan-Tong Li,&nbsp;Xu-Dong Zhao","doi":"10.1111/sapm.70298","DOIUrl":"https://doi.org/10.1111/sapm.70298","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we develop a unified framework based on generalized principal eigenvalues to study spreading speeds in time-heterogeneous nonlocal diffusion models. First, for time-heterogeneous environments with a positive uniform mean value, we investigate the properties and interrelationships of three types of generalized principal eigenvalues and establish sign criteria for them. Next, we use these signs to select appropriate test functions and explicitly construct upper and lower solutions on unbounded domains, thereby characterizing spreading speeds in two scenarios. One concerns a Fisher-KPP equation with compactly supported initial data, and the other involves predator–prey systems with Holling-type I–III functional responses, considering both coinvasion and predator-invasion initial data. Overall, this framework offers an alternative perspective for quantifying the spatiotemporal evolution of solutions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872105","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":"Network Reduction and Absence of Hopf Bifurcations in Dual Phosphorylation Networks With Three Intermediates","authors":"Elisenda Feliu,&nbsp;Nidhi Kaihnsa","doi":"10.1111/sapm.70268","DOIUrl":"https://doi.org/10.1111/sapm.70268","url":null,"abstract":"<p>We show that the removal of a type of reverse reactions preserves the absence of Hopf bifurcations in mass-action reaction networks, or more precisely, the absence of single pairs of purely imaginary eigenvalues of the Jacobian of the system. The motivation is to answer the open question of whether the dual phosphorylation mechanism requiring two encounters of the enzyme and the substrate for both phosphorylation and dephosphorylation admits periodic trajectories. With the tools of model reduction, we provide evidence in favor of the absence of oscillations of this network by precluding Hopf bifurcations in any reduced network comprising three out of its four intermediate protein complexes. Our argument relies on a detailed analysis of the semi-algebraic conditions precluding Hopf bifurcations obtained from Hurwitz determinants of the characteristic polynomial of the Jacobian of the reduced network.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872104","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}