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Communications in Mathematical Sciences最新文献

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IMEX variable step-size Runge-Kutta methods for parabolic integro-differential equations with nonsmooth initial data 具有非光滑初始数据的抛物整微分方程的 IMEX 可变步长 Runge-Kutta 方法
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a6
Wansheng Wang, Mengli Mao, Zifeng Li
{"title":"IMEX variable step-size Runge-Kutta methods for parabolic integro-differential equations with nonsmooth initial data","authors":"Wansheng Wang, Mengli Mao, Zifeng Li","doi":"10.4310/cms.2024.v22.n6.a6","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a6","url":null,"abstract":"We develop a class of implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving parabolic integro-differential equations (PIDEs) with nonsmooth initial data, which describe several option pricing models in mathematical finance. Different from the usual IMEX RK methods, the proposed methods approximate the integral term explicitly by using an extrapolation operator based on the stage-values of RK methods, and we call them as IMEX stage-based interpolation RK (SBIRK) methods. It is shown that there exist arbitrarily high order IMEX SBIRK methods which are stable for abstract PIDEs under suitable time step restrictions. The consistency error and the global error bounds for this class of IMEX Runge-Kutta methods are derived for abstract PIDEs with nonsmooth initial data. The related higher time regularity analysis of the exact solution and stability estimates for IMEX SBIRK methods play key roles in deriving these error bounds. Numerical experiments for European options under jump-diffusion models and stochastic volatility model with jump verify and complement our theoretical results.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"130 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the relaxation process in a class of non-equilibrium two-phase flow models 关于一类非平衡两相流模型松弛过程的说明
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a2
Jean-Marc Hérard
{"title":"A note on the relaxation process in a class of non-equilibrium two-phase flow models","authors":"Jean-Marc Hérard","doi":"10.4310/cms.2024.v22.n6.a2","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a2","url":null,"abstract":"We focus here on the relaxation process in a class of two-phase flow models, considering first gas-liquid flows, and then liquid-vapour mixtures. The whole analysis enables to exhibit a few conditions on the flow in order to guarantee the time decay of some variables. The former may depend on initial conditions but also on equations of state within each phase. The present analysis aims at providing some better understanding of inner processes, and it is also useful for numerical purposes, as emphasized in appendix B. It is a sequel of paper [J.M. Hérard and G. Jomée, ESAIM Proc. Surv., 72:19–40, 2023] where the sole pressure relaxation process in some multiphase flow models is investigated.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The hydrostatic limit of the Beris-Edwards system in dimension two 二维贝里斯-爱德华兹系统的静水极限
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a11
Xingyu Li, Marius Paicu, Arghir Zarnescu
{"title":"The hydrostatic limit of the Beris-Edwards system in dimension two","authors":"Xingyu Li, Marius Paicu, Arghir Zarnescu","doi":"10.4310/cms.2024.v22.n6.a11","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a11","url":null,"abstract":"We study the scaled anisotropic co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in dimension two. We prove the global well-posedness with small analytic data in a thin strip domain. Moreover, we justify the limit to a system involving the hydrostatic Navier-Stokes system with analytic data and prove the convergence.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"28 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and large time behavior for a dissipative variant of the rotational NLS equation 旋转 NLS 方程耗散变体的存在性和大时间行为
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a7
Paolo Antonelli, Boris Shakarov
{"title":"Existence and large time behavior for a dissipative variant of the rotational NLS equation","authors":"Paolo Antonelli, Boris Shakarov","doi":"10.4310/cms.2024.v22.n6.a7","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a7","url":null,"abstract":"We study a dissipative variant of the Gross-Pitaevskii equation with rotation. The model contains a nonlocal, nonlinear term that forces the conservation of $L^2$-norm of solutions. We are motivated by several physical experiments and numerical simulations studying the formation of vortices in Bose-Einstein condensates.We show local and global well-posedness of this model and investigate the asymptotic behavior of its solutions. In the linear case, the solution asymptotically tends to the eigenspace associated with the smallest eigenvalue in the decomposition of the initial datum. In the nonlinear case, we obtain weak convergence to a stationary state. Moreover, for initial energies in a specific range, we prove strong asymptotic stability of ground state solutions.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An efficient interface hydrostatic reconstruction for the two-layer shallow flows with arbitrary wet-dry fronts 具有任意干湿前沿的两层浅层流的高效界面静力学重构
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a9
Jian Dong, Dingfang Li
{"title":"An efficient interface hydrostatic reconstruction for the two-layer shallow flows with arbitrary wet-dry fronts","authors":"Jian Dong, Dingfang Li","doi":"10.4310/cms.2024.v22.n6.a9","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a9","url":null,"abstract":"This paper aims to propose a well-balanced positivity-preserving numerical scheme for the two-layer shallow water systems with arbitrary wet-dry fronts based on interface hydrostatic reconstructions (IHR). One key difficulty in solving the two-layer shallow water systems is the nonconservative product term which cannot be evaluated on the cell boundaries. Another difficulty is that the well-balanced property for the still water maybe missed when the computational domain has wet-dry fronts, especially, the wet-dry front is located at the discontinuous bottom topography. For the nonlinear stability of the numerical scheme, the positivity of the water height is vital. To this end, we discretize the nonconservative product term based on the IHR method, which is a particular choice of path-conservative methods. The intermediate bottom level used in the discretization of the bed source term of two layers is different. The nonconservative product term due to the momentum exchange between two layers is discretized using the intermediate interface water height. The resulting numerical scheme can preserve the positivity of two-layered heights and maintain the still water even when the computational domain has wet-dry fronts. The numerical scheme performs well in solving the complex problems, such as the Kelvin-Helmholtz instable problems. We demonstrate these properties of the current scheme through several classical problems of the two-layer shallow water systems with arbitrary wet-dry fronts.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on enhanced dissipation of time-dependent shear flows 关于随时间变化的剪切流的增强耗散的说明
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a10
Daniel Coble, Siming He
{"title":"A note on enhanced dissipation of time-dependent shear flows","authors":"Daniel Coble, Siming He","doi":"10.4310/cms.2024.v22.n6.a10","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a10","url":null,"abstract":"This paper explores the phenomena of enhanced dissipation in solutions to the passive scalar equations subject to time-dependent shear flows. The hypocoercivity functionals with carefully tuned time weights are applied in the analysis. We observe that as long as the critical points of the shear flow vary slowly, one can derive the sharp enhanced dissipation estimates, mirroring the ones obtained for the time-stationary case.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Machine learning methods for autonomous ordinary differential equations 自主常微分方程的机器学习方法
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a1
Maxime Bouchereau, Philippe Chartier, Mohammed Lemou, Florian Méhats
{"title":"Machine learning methods for autonomous ordinary differential equations","authors":"Maxime Bouchereau, Philippe Chartier, Mohammed Lemou, Florian Méhats","doi":"10.4310/cms.2024.v22.n6.a1","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a1","url":null,"abstract":"Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain computationally expensive: In this paper, we resort to the theory of modified equations in order to obtain “on the fly” cheap numerical approximations. The recipe consists in approximating, prior to that, the modified field associated to the modified equation by <i>neural networks</i>. Elementary convergence results are then established and the efficiency of the technique is demonstrated on experiments.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"7 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global smooth solutions to the two-dimensional axisymmetric Zeldovich-von Neumann-Döring combustion equations with swirl 带漩涡的二维轴对称塞尔多维奇-冯-诺伊曼-多林燃烧方程的全局平稳解
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a5
Honghua Chen, Geng Lai, Wancheng Sheng
{"title":"Global smooth solutions to the two-dimensional axisymmetric Zeldovich-von Neumann-Döring combustion equations with swirl","authors":"Honghua Chen, Geng Lai, Wancheng Sheng","doi":"10.4310/cms.2024.v22.n6.a5","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a5","url":null,"abstract":"This paper studies the two-dimensional (2D) Zeldovich-von Neumann-Döring (ZND) combustion equations with initial data, which are a combination of an axisymmetric flow in a ring and vacuum in the remaining domain. Existence of a global-in-time smooth solution to the initial value problem is obtained by the method of characteristic decomposition, provided that the initial data satisfy some sufficient conditions. The large-time behavior of the solution is also studied. As a result, at any time, the ring continues to expand until the gas burns out in infinite time for the system. The solution describes a phenomenon of the expansion of 2D reacting flows with swirl in vacuum or a phenomenon of “fire whirl”.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localization and the landscape function for regular Sturm-Liouville operators 正则 Sturm-Liouville 算子的定位和景观函数
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-18 DOI: 10.4310/cms.2024.v22.n6.a12
Mirza Karamehmedović, Faouzi Triki
{"title":"Localization and the landscape function for regular Sturm-Liouville operators","authors":"Mirza Karamehmedović, Faouzi Triki","doi":"10.4310/cms.2024.v22.n6.a12","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n6.a12","url":null,"abstract":"We consider the localization in the eigenfunctions of regular Sturm-Liouville operators. After deriving non-asymptotic and asymptotic lower and upper bounds on the localization coefficient of the eigenfunctions, we characterize the landscape function in terms of the first eigenfunction. Several numerical experiments are provided to illustrate the obtained theoretical results.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The gravitational Vlasov-Poisson system with infinite mass and velocities in $mathbb{R}^3$ 在 $mathbb{R}^3$ 中具有无限质量和速度的引力弗拉索夫-泊松系统
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2024-07-15 DOI: 10.4310/cms.2024.v22.n5.a11
Guido Cavallaro, Carlo Marchioro
{"title":"The gravitational Vlasov-Poisson system with infinite mass and velocities in $mathbb{R}^3$","authors":"Guido Cavallaro, Carlo Marchioro","doi":"10.4310/cms.2024.v22.n5.a11","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n5.a11","url":null,"abstract":"We study existence and uniqueness of the solution to the gravitational Vlasov–Poisson system evolving in $mathbb{R}^3$. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law. We extend a classical result which holds for systems with finite total mass.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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